A statement from his family said the star died in the early hours of Saturday "surrounded by his family", reported BBC News.
"He has been in poor health for some time, but was cracking jokes to the last," the family added.
Mitchell's great nephew paid tribute to him on Twitter, saying he was "the last of his generation".
The full tweet read: "Just got the news my great uncle Warren Mitchell (aka Alf Garnett) died last night. The last of his generation, wonderful and funny man RIP."
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He returned as Alf Garnett in the BBC series "In Sickness and in Health", which ran from 1985 to 1992.
He also received critical acclaim for other roles. He won Olivier Awards for his stage performances in Arthur Miller's "Death of a Salesman" in 1979 and "The Price" in 2004.
Born in north London's Stoke Newington, he served in the Royal Air Force and then went on to read physics at University College, Oxford.
Mitchell appeared in "Till Death Us Do Part" with Una Stubbs and Tony Booth. In 2004 he suffered from a stroke, but was back performing in Miller's "The Price" a week later.
He also appeared in TV shows including "Gormenghast", "Wall of Silence", "Lovejoy", "Waking The Dead" and "Kavanagh QC".
Celebrities paid their tributes to the actor. Comedian Ricky Gervais tweeted: "Alf Garnett was one of the most influential and important characters and performances in comedy history. RIP Warren Mitchell."
Theatre director Rupert Goold wrote: "RIP Warren Mitchell. A deeply soulful and erudite man who genuinely loved the theatre."
Mitchell is survived by his wife Constance Wake, a fellow actress, and three children.