"The invitation has been extended and has been accepted," a Number 10 spokesperson told IBTimes UK.
The comments come as thousands of people plan to stage a protest in Whitehall over the US president's travel ban.
The executive order blocks those from Iran, Iraq, Sudan, Syria, Yemen, Libya and Somalia from travelling to America for 90 days.
Number 10 later said May "doesn't agree" with Trump's clampdown and Foreign Secretary Boris Johnson, who described the initiative as "divisive", was able to win some exemptions from the Republican administration.
Johnson's intervention means the order will only apply to those travelling directly from the seven listed countries to the US.
UK citizens who hold dual-nationality with the blacklisted nations will not face extra checks unless they travel directly from the seven Muslim-majority countries to America.
"The US has reaffirmed its strong commitment to the expeditious processing of all travellers from the UK," a Foreign Office spokesperson said.
The row comes just days after May became the first foreign leader to meet Trump in the White House.
But now more than a million people have now signed an online petition in a bid to block the US president from travelling to Britain to meet The Queen.
The cross-party Petitions Committee will decide whether MPs will debate the petition.
May, meanwhile, will chair Brexit talks in Cardiff with Scotland's Nicola Sturgeon and Welsh First Minister Carwyn Jones.
The Joint Ministerial Committee is the first to take place outside of London and comes after the government tabled its Article 50 bill in parliament following a defeat at the Supreme Court.