Forman passed away on Friday in the USA after a short illness, his wife, Martina, told Czech news agency CTK.
Forman first attracted global attention with such features as Black Peter (1964), The Loves of a Blonde (1965) - an Oscar nominee for best foreign-language film - and The Firemen's Ball (1967), which put him in hot water with the communist regime in Czechoslovakia.
In August 1968, just days before the Soviet-led crackdown that followed the Prague Spring uprising, Forman left Czechoslovakia for France, moving to the United States a few months later.
After struggling to find further work in the USA, he was eventually hired by producers Michael Douglas and Saul Zaentz to direct their 1975 adaptation of Ken Kesey's One Flew Over the Cuckoo's Nest. Forman then had another huge success with Amadeus, a film version of Peter Shaffer's play about the rivalry between Mozart and Salieri; it won eight Oscars, including Forman's second for best director.
Forman, also known for two biopics about controversial Americans - The People vs. Larry Flynt (1996) and Man on the Moon (1999) - died Friday in the US after a short illness, according to his wife, Martina, who broke the news to the Czech news agency CTK.
Hunting for locations, Forman realized Prague was the only European capital that had changed little since Mozart's time, but returning there initially filled him with dread.
Forman, by then an American citizen, returned to film the drama nearly entirely in Czechoslovakia.
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"I was used to seeing the Russian and Czech films about composers, and they were the most boring films", he said.
Forman rebounded four years later with the iconic "One Flew Over the Cuckoo's Nest", which won five Academy Awards, including one for himself as director.
In his biography, Forman wrote, "My parents were real patriots, and that was probably the reason why they died". He also shot a film version, released internationally in 2009.
Born to a Protestant family in the central Czech town of Caslav on February 18, 1932, the double Oscar winner's life was indelibly scarred by World War II.
The director's first marriage, to actress Jana Brejchova ended in divorce.
Man on the Moon, based on the life of cult hero Andy Kaufman, did win its star, Jim Carrey, a Golden Globe.
In 1999, he married screenwriter Martina Zborilova with whom he also had twin sons, Andrew and James.