The landscape gardener died when his car left the road and rolled before landing on its side on the A34 in Gatley, Cheadle, Greater Manchester Police said.
He was the only person in the white Volkswagen Golf R estate and was taken to hospital, where he died from his injuries on 29 May.
Mr Gardiner and his mother travelled across Mexico and Argentina in the BBC show, broadcast in March 2020.
His father Andrew said: "When the news broke last week, friends asked how they could help.
"After some thought, I decided to set up a JustGiving page to raise money for National FASD in memory of Sam.
"The page is called Sam Gardiner; Super Human."
He said it was "very humbling to see the Race Around The World family rally to this worthy cause".
A message on its official Instagram account said: "Sam lived his life full of love, exuberance and adventure as seen on BBC's Race Across the World.
"National FASD is both humbled and honoured to help carry on his legacy via donations coming from hundreds."
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