The 1975 adaptation of Ken Kesey's novel, One Flew Over the Cuckoo's Nest, secured Forman his first Best Director win at the Academy Awards.
Forman's manager Dennis Aspland confirmed to the Press Association that he had been told by the director's wife Martina that he had "passed away late last night".
When Soviet tanks rumbled into Prague in August 1968, Forman was in Paris for negotiations on his first American production and was sacked by his Czech studio, leading him to emigrate.
Forman's other English-language films included 1996's The People vs Larry Flynt, which earned him his third best director Oscar nomination, and 1999's Man on the Moon.
Forman's friends had questioned him about his decision to direct "One Flew Over the Cuckoo's Nest", a story they said was "so American" for a foreign director.
Three years later while Forman was in bed with a fever, the Gestapo intruded again, this time at the family home.
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The Czech news agency CTK quoted Martina Forman as saying her husband died suddenly on Friday after a short illness.
In 1983, he made his second Oscar-winning film Amadeus, starring Tom Hulce as Wolfgang Amadeus Mozart. "And right there after the show, I met for the first time Peter Shaffer, and I told him that if he would ever consider making a movie, I would be very interested". Both his parents were killed in Nazi concentration camps during World War II, according to Forman's official biography.
"A director is little bit of everything, little bit of the writer, little bit of an actor, little bit of an editor, little bit of a costume designer", Forman once said.
He remained connected to his birth country, filming "Amadeus" there.
The director's first marriage, to actress Jana Brejchova ended in divorce.
Forman (c.) directed Danny DeVito (l.) and Jim Carrey (r.) in the Andy Kaufman biopic "Man on the Moon".