their dog was also found dead
In a career that spanned more than six decades, he received two Academy Awards, two Baftas, four Golden Globes and a Screen Actors Guild Award.
A statement from the Santa Fe County Sheriff in New Mexico said: "We can confirm that both Gene Hackman and his wife were found deceased Wednesday afternoon at their residence on Sunset Trail.
Hackman won the best actor Oscar for his role as Jimmy "Popeye" Doyle in William Friedkin's 1971 thriller The French Connection, and another for best supporting actor for playing Little Bill Daggett in Clint Eastwood's Western film Unforgiven in 1992.
His other Oscar-nominated roles were in 1967 movie Bonnie and Clyde - as Buck Barrow in his breakthrough role - and 1970's I Never Sang for My Father, as well as playing the agent in Mississippi Burning (1988).
Santa Fe County Sheriff Adan Mendoza confirmed the news to local media just after midnight on Wednesday that the couple had died, along with their dog.
The news was later confirmed to the Press Association news agency. Hackman was 95 and his wife 63.
Mr Mendoza said there was no immediate indication of foul play.
But he did not provide a cause of death or say when the couple might have died.
"All I can say is that we're in the middle of a preliminary death investigation, waiting on approval of a search warrant."
Much celebrated actor Hackman played more than 100 roles including Lex Luthor in Superman movies in the 1970s and 1980s.
He also starred in the hit movies Runaway Jury and The Conversation, as well as Wes Anderson's The Royal Tenenbaums.
His last big screen appearance came as Monroe Cole in Welcome to Mooseport in 2004.
Born in California in 1930, Hackman had enlisted in the army after lying about his age at 16, serving for four-and-a-half years.
Following his military service, after briefly living in New York he decided to pursue acting.
In order to pursue his chosen career, Hackman joined the Pasadena Playhouse in California, where he befriended a young Dustin Hoffman.
"I was trained to be an actor, not a star. I was trained to play roles, not to deal with fame and agents and lawyers and the press," he once said.
"It really costs me a lot emotionally to watch myself on-screen. I think of myself, and feel like I'm quite young, and then I look at this old man with the baggy chins and the tired eyes and the receding hairline and all that."
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