Forman first attracted worldwide attention with features like "Black Peter", "The Loves of a Blonde" (1965) - an Oscar nominee for best foreign-language film and "The Firemen's Ball". He had been in Paris when the communists crushed the Prague Spring movement in 1968, and he hadn't bothered to return home, becoming a USA citizen in 1975.
His first American movie, Taking Off, picked up the 1971 Grand Prix at the Cannes Film Festival, and his 1976 film One Flew Over the Cuckoo's Nest, starring Jack Nicholson, won five Oscars, including Best Picture and Best Adapted Screenplay, while Forman scooped the Best Director honour.
He followed up his success in 1979 with a film adaptation of the hit musical "Hair", and then in 1981 with an adaptation of E. L. Doctorow's novel "Ragtime".
He earned a third nomination for 1996's "The People vs. Larry Flynt", a depiction of the porn magazine publisher's protracted legal fight for First Amendment rights.
"I was used to seeing the Russian and Czech films about composers, and they were the most boring films", he said.
Forman was born in the Czech Republic in 1932.
Forman is survived by his wife, Martina Zborilova-Forman, and four children.
Writer and producer Larry Karaszewski, who made Man On The Moon and The People vs Larry Flynt with Forman, wrote: "Milos Forman was our friend and our teacher".
Valmont, Forman's 1989 adaptation of Les Liaisons Dangereuses, proved something of an anticlimax as another version, directed by Stephen Frears and containing a star-making performance from John Malkovich, had been released the previous year.
He was raised an orphan after both his parents died in concentration camps during World War Two.
A cigar-puffing cycling enthusiast who always retained a heavy accent, Forman was married to actresses Jana Brejchova and Vera Kresadlova. They were named after comedian Andy Kaufman and Jim Carrey, who played the part of Kaufman in "Man on the Moon".