Report shows police carried out computer checks to "impugn those who died".
Cameron: "I am profoundly sorry".
Former Sun editor Kelvin MacKenzie offers his "profuse apologies" over paper's coverage of events.
A copy of the report delivered by the Hillsborough Independent Panel is positioned next to a copy of today's Liverpool Echo (Reuters)
Sheffield-based news agency Whites, who Cameron revealed was behind the Sun's original reporting of the story in 1989 along with then MP for Sheffield Hallam Patnick, have released a statement.
It reads: "Several reporters from this agency had some involvement in covering the Hillsborough tragedy and the aftermath.
"In common with many other journalists, reporters from this agency spoke to the then Sheffield Hallam MP Irvine Patnick.
"A senior reporter, who has since died, and with long-standing police connections, also spoke to senior officers.
"As result, as a responsible and reputable agency, we did report the allegations to all the national newspapers and media outlets.
"The agency had no control over how the allegations were presented and were shocked by the way the story was presented by the Sun. Other newspapers reported the allegations in a different way.
"We welcome the publication of all documents relating to the Hillsborough tragedy and hope it brings some measure of closure for those affected. We have no further comment to make."
16:22 Steven Gerrard has also released a statement this afternoon on the official Liverpool website. it reads: "The courage and dignity shown by the Hillsborough families and survivors is an example to all of us.
"For 23 years they have fought for truth and justice on behalf of the victims and survivors of this terrible tragedy and all Liverpool supporters.
"Victims and survivors suffered not just on April 15, 1989 in Sheffield, but for over two decades afterwards with the shameful slandering of their actions by people who abused their position and power.
"Speaking as someone whose family directly suffered, I know the pain and hurt will remain.
"However, I hope that today's report helps bring some comfort, now that everyone knows what happened on that day."
Hillsborough Family Support Group lawyer, James Saunders of Saunders Law, has demanded attorney general scraps the original inquest verdicts and calls for a new one.
He said: "I am privileged to act for the Hillsborough Family Support Group who have campaigned with persistence and great dignity over many years for the truth to be told about the Hillsborough tragedy. The HIP report published today is a truly damning indictment of officials and processes that have concealed the truth about Hillsborough for so long.
"The very people charged with looking after the safety of those Liverpool FC fans who died not only allowed and caused what happened, but then lied to avoid the blame, and cruelly blamed the victims for the failures.
"The welcome statements today by David Cameron and politicians from all parties start the healing process, but a new inquest is required. The families and the public deserve this.
"It is for Dominic Grieve, the attorney general, to make an application to the high court to quash the current inquest verdict which was based on evidence that had been tampered with, and an untrue picture of events. Only then can a new inquest look to find the truth in public as is required.
"I would want to properly consider the vast body of new evidence before taking other steps, but it may well be that those persons who have lied, concealed and distorted evidence should now be brought to account before the law personally."
South Yorkshire Police have released a statement apologising for the day's events, saying how police that day had "lost control".
The statement says: "On 15th April 1989, 96 of the Liverpool fans went to Hillsborough to watch the FA Cup Semi Final and died as a result of the disaster.
"On that day South Yorkshire Police failed the victims and families. The police lost control. In the immediate aftermath senior officers sought to change the record of events.
"Disgraceful lies were told which blamed the Liverpool fans for the disaster.
"Statements were altered which sought to minimise police blame. These actions have caused untold pain and distress for over 23 years.
"I am profoundly sorry for the way the force failed on 15th April 1989 and I am doubly sorry for the injustice that followed and I apologise to the families of the 96 and Liverpool fans.
"South Yorkshire Police is a very different place in 2012 from what it was 23 years ago and we will be fully open and transparent in helping to find answers to the questions posed by the Panel today."
A reporter asks Michael Mansfield QC if this is the biggest cover-up in British history. He replies: "Quite simply, yes."
Here's a video of MacKenzie refusing to apologise for Hillsborough in a 2010 edition of Question Time
MacKenzie statement in full: "Today I offer my profuse apologies to the people of Liverpool for that headline. I too was totally misled.
"Twenty three ago I was handed a piece of copy from a reputable news agency in Sheffield in which a senior police officer and a senior local MP were making serious allegations against fans in the stadium.
"I had absolutely no reason to believe that these authority figures would lie and deceive over such a disaster.
"As the prime minister has made clear, these allegations were wholly untrue and were part of a concerted plot by police officers to discredit the supporters thereby shifting the blame for the tragedy from themselves.
"It has taken more than two decades, 400,000 documents and a two-year inquiry to discover to my horror that it would have been far more accurate had I written the headline The Lies rather than The Truth. I published in good faith and I am sorry that it was so wrong."
Kelvin MacKenzie, the editor of The Sun at the time of the tragedy and the man responsible for 'The Truth' headline has offered his "profuse apologies to the people of Liverpool" over it.
Chairman of Hillsborough Families Support Group Trevor Hicks says apology from MacKenzie is "too little, too late ... he's a low-life".
Two-minute silence takes place across Liverpool.
Two minutes silence was held at the time when the game at Hillsborough was abandoned in 1989
Liverpool FC have released a statement on the report.
It reads: "Over the last 23 years the families who lost loved ones and the survivors of this terrible tragedy have shown immense dignity and resilience in their tireless campaign for justice.
"For 23 years they have campaigned for the full disclosure of documents relating to the disaster and for someone to take responsibility for what happened.
"Today, following years of inquiries, investigations and setbacks, the Hillsborough Independent Panel has announced its findings in relation to the disaster.Liverpool Football Club commends the Hillsborough Independent Panel report which acknowledges the avoidable catastrophic failures before, during and after the disaster.
"The club also welcomes the prime minister's apology to the families and survivors on behalf of the Government and await the attorney general's pending review of the report. After 23 long and painful years, our fans have finally been fully exonerated of all blame.
"Today, the world knows what we have always known, that Liverpool fans were not just innocent on that terrible day but that there was reprehensible and hurtful misrepresentation of the truth.
"Liverpool Football Club would like to thank the Hillsborough Independent Panel for its rigorous work over the past two-and-a-half years and for publishing a comprehensive report based on the in-depth research and analysis into hundreds of thousands of documents.
Margaret Aspinall tells a news conference Liverpool fans had "saved people's lives" that day and have nothing to be ashamed about.
Sky News announces Kelvin MacKenzie is due to make a statment this afternoon.
News conference of the victim's familes now taking place
Reminder of the main points:
The Hillsborough Independent panel explained up to 41 of the 96 people who died had the potential to survive but were declared dead by the original coroner at 3:15.
The Sun's controversial 'The Truth' story originally came from a Sheffield news agency.
South Yorkshire police altered 164 statements and removed 166 negative comments about how the police operated the disaster.
Police carried out checks on those who had died in order to "impugn their reputations"
The conference has now ended. Families of the victims will now get the chance to speak to the panel in a private meeting.
Margaret Aspinall, chairwoman of the Hillsborough Families Support Group, whose 18-year-old son James was killed, said: "This is what the families and the fans have been fighting for for 23 years. Without the truth, you cannot grieve and where there is deceit, you get no justice."
Professor Phil Scraton on the panel: "To see every member of the families standing and applauding the work of the panel, to me that was a clear indication that we have done the right thing."
Nick Garnett of BBC 5 Live tweets:
Bishop Jones: Families will be able to interrogate all members of panel on one-to-one basis. All panel members have brought different skills to table in our search for truth and justice.
Bishop James Jones says it is not for the HIP to decide if there was a cover-up on that day.
Margaret Aspinall, Chairman of the Hillsborough Families Support Group, whose 18-year-old son James was killed, told AP: ""This is what the families and the fans have been fighting for, for 23 years. Without the truth, you cannot grieve and where there is deceit, you get no justice,"
Original copy of the Hillsborough disaster report as filed by Sheffield's White's news agency can be seen here:
It begins with: "Angry police hit back yesterday at Liverpool fans who hampered life saving attempts after Hillsborough horror."
Statement from Shelia Coleman, spokeswoman for the Hillsborough Justice Campaign.
She said: "We were aware of an awful lot of what was said by the panel because we were party to those actions.
"We were also disgusted when Norman Bettison's name was revealed. We petitioned and had a sit-in at Merseyside police authority, pleading with them not to appoint him.
We now find out he was part of the police federation which had a strategy to blame drunken, ticketless fans and then leaked it it the MP who leaked it to the press agency and that was how [The Sun editor Kelvin] Mackenzie got it.
"The findings are shocking in terms of the blood alcohol tests and the police computer being activated to look for criminal activity.
"These were criminal activities. We have got to the truth but where is the justice? That is what is crucial now. It will be even more frustrating if nothing else happens.
"We want the inquest verdict to be overturned with urgency in all cases. We will be pushing for that and pursuing it legally and having all documents looked over by our own legal team.
"Where I am disappointed is there was no mention of Margaret Thatcher, Bernard Ingham or Colin Moynihan or the government's role in the cover-up.
"The Thatcher government is getting away scot-free. It is not highlighted at all. The blame is being laid at the door of the police and ambulance service.
"We are pleased with what has happened so far but disappointed with that.
"It was truly shocking to hear people could have been saved. There are so many shocking aspects. But the fans were totally vindicated."
Hillsborough Independent Panel members attend a news conference in Liverpool's Anglican Cathedral, in Liverpool (Reuters)
The HIP: "Up to 41 people could have been saved had there been no 3.15 deadline at Hillsborough".
HIP have started their press conference led by the Bishop of Liverpool, the Right Reverend James Jones.
The conference began with a moment of silence to remember the victims.
The Sun newspaper's Twitter account has tweeted twice since David Cameron's speech. Here's one:
And here's the second:
This is what Cameron said about the coroner's decision on the times of death:
"The Bishop of Liverpool's report presents new evidence which casts significant doubt over the adequacy of the original inquest.
The coroner - on the advice of pathologists - believed that victims suffered traumatic asphyxia leading to unconsciousness within seconds and death within a few minutes.
As a result he asserted that beyond 3.15pm there were no actions that could have changed the fate of the victims and he limited the scope of the Inquest accordingly.
But by analysing post mortem reports the panel have found that 28 did not have obstruction of blood circulation and 31 had evidence of heart and lungs continuing to function after the crush.
This means that individuals in those groups could have had potentially reversible asphyxia beyond 3.15pm in contrast to the findings of the coroner and a subsequent judicial review.
And the panel states clearly that 'it is highly likely that what happened to those individuals after 3.15pm was significant' in determining whether they died."
The Hillsborough Independent Panel are now due to hold a news conference following today's revelations.
Merseyside MP Maria Eagle thanks Cameron, but asks "is it not indicative of a failure in our legal system" that important documents and facts have only just been released and seen.
A press conference with the some of the victims' families is due to take place.
Ed Miliband calls for an apology from the Sun newspaper
Ed Miliband: "The disaster was caused not by fans but by an unsafe ground and negligent policing. Original inquest was hopelessly inadequate.
"Today's report is black and white: the Liverpool fans were NOT the cause of the disaster"
David Blunkett, the former home secretary and Sheffield MP, tells MPs: "No one in their right mind could have blamed the victims".
David Cameron has said he is "profoundly sorry"
David Cameron: The conclusions will be "very harrowing".
Coroner's decision to regard 3.15pm as time after which no victims could be saved was wrong. Nearly 60 victims were still alive after that time with injuries that could have been reversed. They could have been saved, he said.
"Safety of the crowd at Hillsborough was compromised at every level.
"164 statements were significantly amended, and 116 had negative comments of police reaction removed.
"Blood alcohol checks were made on the victims, including children.
"The panel found no evidence of the government trying to conceal the truth.
"The source of these allegations was a Sheffield news agency, which was acting on police efforts to propagate myths of drunkenness and violence
"The families have not heard the truth and have not found justice. It was right the families should see these papers.
"It is already very clear many of the reports find are deeply disturbing."
The documents have already been released to the families of the victims.
PMQS has started in the House of Commons.
A press conference from the Hillsborough Independent Panel is due to be announced after Cameron's statement at 12:30
Luke Traynor, journalist at the Mirror has tweeted:
Arif Ansari, BBC's north west politicasl editor, has tweeted: "Downing Street says David Cameron now has a copy of the Hillsborough report which he received shortly before 1100" Full statement expected from the Prime Minister at 12:30
Sheffield Wednesday, who play at Hillsborough Stadium, has already released a public apology for the tragedy.
It said: "Sheffield Wednesday FC welcomes the release of the Hillsborough Independent Panel report and would like to acknowledge the enormous amount of hard work by all involved during what was, and continues to be, an extremely emotive process.
"Throughout the compilation stage, the club has worked closely with the panel and the other donating organisations to ensure that, in line with the ethos of maximum disclosure, we have been totally transparent.
"Sheffield Wednesday would also like to record its gratitude for the thoroughly dignified manner with which the Hillsborough Family Support Group and its representatives conducted themselves throughout all levels of consultation with the club.
"Since the acquisition of Sheffield Wednesday Football Club in December 2010 and the subsequent decision of the previous board to dissolve the former parent company Sheffield Wednesday PLC , chairman Milan Mandaric and the current board of directors have adopted a policy of complete compliance with the requests of the Hillsborough Independent Panel and on behalf of the club would like to offer our sincere condolences and an apology to all the families who have suffered as a consequence of the tragic events of 15 April, 1989.
"We can only hope that the publication of the Hillsborough Independent Panel report goes some way to providing the closure sought by all those involved.
"The thoughts of everyone at Sheffield Wednesday FC remain with the 96 Liverpool supporters who lost their lives, their families, and the wider Liverpool community who have all been affected so deeply by the disaster of 23 years ago.
David Cameron is expected to issue an apology in the House of Commons later after PMQs.
Today, 23 years, four months and 28 days after the Hillsborough disaster which claimed the lives of 96 people, the families of the victims will get the see the hundreds of thousands of official into the incident.
The Hillsborough Independent Panel has spent the last 18 months probing through the papers and will have will release an official report today.
LiverpoolEchofrontpage: '96 reasons for the truth'
A 1990 report into the tragedy, led by Lord Justice Taylor, concluded that the main reason for the disaster was a failure by South Yorkshire Police to control the crowd.
The documents have already been seen this morning by the victim's families at Liverpool's Anglican Cathedral and will be released later to the public.