Cimino, 77, who directed a total of eight films, will be remembered for a career of highs and lows.
While The Deer Hunter has been hailed as one of the best movies in recent Hollywood history, his next project, Heaven`s Gate, was derided as a flop.
Eric Weissmann said Cimino`s body was found at his Los Angeles home on Saturday after friends had been unable to contact him. No cause of death has yet been determined.
News of the director`s death was first tweeted by Cannes Film Festival director Thierry Fremaux (in French).
The Deer Hunter with its famous Russian roulette scene starred Robert de Niro and Christopher Walken and won five Oscars including the award for the best film in 1979.
It chronicles the lives of a group of friends from a Pennsylvania town and the devastating effect of the Vietnam War, both on those who fought in it and those who stayed at home in small-town America.
Based on this success, Cimino wrote and directed Heaven`s Gate, loosely based on the Wyoming Johnson County war of 1889-93.
It was a financial disaster that went four times over budget and a year behind schedule, It nearly bankrupted the United Artists studio.
But the film - starring Christopher Walken and Kris Kristofferson and - has more recently been hailed as a masterpiece.
Cimino in his earlier career was an advertising executive who moved into film with the Clint Eastwood and Jeff Bridges crime caper, Thunderbolt and Lightfoot, in 1974.
He also directed Desperate Hours (1990), starring Mickey Rourke and Anthony Hopkins, and the gangster film The Sicilian (1986), adapted from a novel by Godfather author Mario Puzo.
Correspondents say Heaven`s Gate led to the demise of director-driven productions in the late 1970s and the imposition of tighter controls on film budgets.
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