The 27-year-old entrepreneur and TV contestant was found dead at his Isle of Man home on 30 July.
He became the youngest-ever candidate to appear on the hit BBC One show in 2010, aged 21.
Baggs made it to the semi-final of the show and became known for his memorable one liners, such as "Everything I touch turns to sold" and "I'm Stuart Baggs the brand."
The post-mortem following his "sudden and unexpected" death was carried out last week, with police saying there were no suspicious circumstances.
A statement issued by the Isle of Man Constabulary on 6 August said: "Mr Baggs had suffered from asthma for many years and died as a result of his condition."
Inspector Michelle McKillop said: "From the reaction we have encountered during our inquiries it is clear that this is a tragic and premature loss of such a hardworking and visionary young man.
"We extend our thoughts to the family at this sad time and on their behalf I would request that they are now left in peace to grieve as a family."
Baggs lived in the Isle of Man for most of his life, where he headed a telecommunications company.
In an interview with the Isle of Man Examiner days before his death, he said: "I work, as my hair will tell you, at least 18 hours a day.
"I sleep for four hours religiously, I would not have it any other way, like Margaret Thatcher."
On 6 August, Asthma UK released a statement urging sufferers to be alert to the early symptoms of attacks.
"Our thoughts are with Stuart Baggs' family and friends at such a heart-breaking time.
"Many people don't realise how serious asthma is yet every ten seconds someone in the UK is having a potentially life threatening asthma attack and sadly three people die every day," said Dr Samantha Walker, the charity's Deputy Chief Executive.
"I can't stress enough how important it is that people with asthma recognise the early warning signs of an asthma attack and know what to do when their symptoms are getting worse."