He was found dead of natural causes at his home in Brentwood, Los Angeles.
Police officers responded to a call at around 8pm local time and confirmed Garner’s identity from family members.
There was no immediate word on a specific cause of death.
Garner had suffered a stroke in May 2008, just weeks after his 80th birthday but had made a recovery.
He starred in 1963’s much loved Second World War film The Great Escape, in which he played flight lieutenant Robert Hendley, an American in the RAF, alongside Steve McQueen, Richard Attenborough and Donald Pleasence.
Although he was adept at drama and action, Garner was best known for his witty, low-key style, especially in Maverick and The Rockford Files. He was nominated for an Oscar for the 1985 movie Murphy’s Romance and won an Emmy award in 1977.
Garner remained active well into his 70s and received the highest honour of the Screen Actors Guild in 2004.
During an interview on US television in 2000 he remarked that he was “always nervous” when acting, adding: “I’ve never been that confident, I don’t have the background in acting.”
Prior to becoming an actor he served in the Korean war and was injured in 1951. He received a Purple Heart medal in 1983.
He is survived by his wife, Lois. They married in 1956 just two weeks after first meeting.
The actor had one daughter with Lois, Greta ‘Gigi’ Garner, and one half-daughter from his wife’s previous marriage, Kimberly.