Czech news agency CTK reported that Forman died on Friday in the United States after a short illness.
The Hollywood Reporter reports that his manager, Dennis Aspland, confirmed Forman's death to The Hollywood Reporter and noted that the filmmaker had a home in Warren, Connecticut.
"One Flew Over the Cuckoo's Nest", adapted from Ken Kesey's 1962 novel, dealt with life inside an OR mental institution.
The film, which starred Jack Nicholson and Louise Fletcher, won five Oscars, including best picture and best director and went on to become the second film in history to win the top five Academy Award categories.
"Amadeus" won eight Academy Awards, including for best picture and for Forman as best director.
"In his films you can see the author", he said.
With some trepidation, Forman returned to Czechoslovakia to make "Amadeus" because Prague was one of the few European cities that had been little changed since Mozart's time.
Miloš Forman, director of 'Amadeus' and 'Cuckoo's Nest,' is dead at 86
Forman was born in Caslav, Czech Republic, in February 1932. Both his parents were killed in Nazi concentration camps during World War II, according to Forman's official biography.
Forman said the film's central issues of censorship and free expression were influenced by his youth in Eastern Europe, when filmmakers and other artists were limited in what they could say by the communist regime.
Forman's unique brand of humor and anti-authoritarian viewpoints were truly unleashed in his film, The Firemen's Ball, which was banned from theaters following the Soviet invasion in August 1968.
Milos Forman poses after being presented with the "Giraldillo" award for his life-long career achievements at Sevilla Festival Film Spain.in 2004.
His other notable films include Hair (1979), Ragtime (1981) and Valmont (1989).
Actor Antonio Banderas also paid tribute to Forman.
Milos leaves behind wife Martina and his four sons - Andrew and James, and twins Matej and Petr Forman from his second marriage to Vera Kresadlova.
Man on the Moon, based on the life of cult hero Andy Kaufman, did win its star, Jim Carrey, a Golden Globe.
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