Clark’s family told TMZ he was an “actor’s actor” who loved and respected his craft but was never interested in celebrity or the trappings of fame.
The family said he died the way he had lived – “on his terms”.
They added Clark had felt “lucky” about the career he built in the film industry.
Director Gary Rosen paid tribute to Clark’s legacy as a performer whose work spanned what he described as a defining period of American film-making.
The film-maker said: “He was the kind of actor that defined Hollywood film-making in its greatest era, the utterly unique character player who made every scene he appeared in memorable, often stealing them from stars like Rod Steiger, Robert Redford, Clint Eastwood and John Wayne.”
Rosen added: “His roles in In the Heat of the Night, Jeremiah Johnson, The Outlaw Josey Wales, The Cowboys, Pat Garrett and Billy the Kid, among many others, helped to elevate those films to classic status. He leaves the stage, but his performances will be remembered forever.”
Across his career, Clark appeared in numerous westerns and dramas.
He acted alongside Redford in Sydney Pollack’s 1972 film Jeremiah Johnson and appeared with Eastwood in films including The Outlaw Josey Wales, The Beguiled and Honkytonk Man.
Clark also appeared in John Wayne’s The Cowboys and Paul Newman’s The Life and Times of Judge Roy Bean.
His other film credits included Brubaker, in which he played Roy Purcell, as well as the cult science-fiction film The Adventures of Buckaroo Banzai Across the 8th Dimension.
On television, he appeared in the sitcom Grace Under Fire.
Clark also directed the 1988 film Da, which starred Bernard Hughes, Martin Sheen and William Hickey.
Speaking in 1991 about his fondness for western films, Clark said: “I just loved ’em! Just like you always wanted to do as a little kid, you put on chaps and boots and tie on spurs that jingle when you walk.”