Jones appeared in the troupe’s TV series and films including Monty Python and the Holy Grail and The Life of Brian.
In 2016 he was diagnosed with frontotemporal dementia.
“We are deeply saddened to have to announce the passing of beloved husband and father, Terry Jones,” his family said in a statement on Wednesday.
The statement said Jones’ wife Anna Soderstrom, children Bill, Sally and Siri, and other relatives and friends had been by his side as the comedian “gently slipped away” at his London home.
“We have all lost a kind, funny, warm, creative and truly loving man whose uncompromising individuality, relentless intellect and extraordinary humour has given pleasure to countless millions across six decades,” they said.
“His work with Monty Python, his books, films, television programs, poems and other work will live on forever, a fitting legacy to a true polymath.
” … We ask that our privacy be respected at this sensitive time and give thanks that we lived in the presence of an extraordinarily talented, playful and happy man living a truly authentic life, in his words ‘Lovingly frosted with glucose’.”
Fellow Python Sir Michael Palin told the BBC Jones was “one of the funniest writer-performers of his generation”.
“We have all lost a kind, funny, warm, creative and truly loving man,” he said.
“Terry was one of my closest, most valued friends. He was kind, generous, supportive and passionate about living life to the full.
“He was far more than one of the funniest writer-performers of his generation, he was the complete Renaissance comedian – writer, director, presenter, historian, brilliant children’s author, and the warmest, most wonderful company you could wish to have.”
Other comedians also paid tribute to Jones online.
The Welsh-born star suffered from primary progressive aphasia, which affected his ability to communicate.
Jones directed Monty Python And The Holy Grail in 1975 with Terry Gilliam.
The group’s Life Of Brian film in 1979, about a hapless man mistaken for Jesus, was attacked as blasphemous at the time but has since been voted the funniest classic comedy in a poll compiled by the magazine Total Film.
On-screen, his much-loved characters included Arthur “Two Sheds” Jackson, Cardinal Biggles of the Spanish Inquisition and Mr Creosote, the monstrously obese restaurant patron.
Jones also directed The Meaning Of Life in 1983, the Pythons’ last film together.
His other credits include The Wind In The Willows in 1996, with performances from Eric Idle, Michael Palin, and John Cleese, 2015 comedy Absolutely Anything, and Personal Services (1987).
Jones had two children with Alison Telfer, who he married in 1970, and became a father again at the age of 67, with second wife Anna Soderstrom.