Parker, who is returning to Britain after a decade in the US, said yesterday he had taken on the role because there was a new government that supported the British film industry.
"The sole reason I've taken the job on is because of the new Government, which I support. Never in my memory have we had a government that has been as engaged with the film industry. It is very enlightened."
His appointment is unlikely to be welcomed by Peter Greenaway, the celebrated director of The Cook, The Thief, His Wife and Her Lover, whose films Parker once said he could make with his eyes shut.
The British Film Institute itself has in the past been a prime target for Mr Parker's disdain. He called it a little fiefdom where "something that's pretentious and shallow and obscure is described as art".
Yesterday he was rather more complimentary, saying: "My criticisms of the British Film Institute were some time ago and then I went off and went to live in America. The BFI is a much unloved and misunderstood institution."
Mr Parker said his core interest would be education. "Maybe we could educate people to go and see more than the next Arnold Schwarzenegger film."
The British Film Industry is the agency charged with promoting and developing the arts of cinema and TV. It said it believed Mr Parker was the right man for the job.
"His knowledge of the industry, skills in film making and dynamism will help the BFI move forward confidently into the 21st Century," said BFI director Wilf Stevenson.
Mr Parker made his name in the Seventies as a director of TV advertisements. His first big film, Bugsy Malone, got him noticed in Hollywood, where he made Fame in 1980. Since then he has made serious films like Birdy and Mississippi Burning, as well as lighter fare, such as The Commitments and Evita. Paul McCann