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, his family said.
“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’.”
With Eric Idle, John Cleese, Michael Palin, Graham Chapman and Terry Gilliam, Jones formed Monty Python’s Flying Circus, whose anarchic humour helped revolutionise British comedy.
Born in Wales in 1942, Jones attended Oxford University, where he began writing and performing with fellow student Michael Palin.
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.
After leaving university, Jones wrote for seminal 1960s comedy series, including The Frost Report and Do Not Adjust Your Set. At the end of the decade he, along with Palin, Idle, Cleese, Chapman and Gilliam, formed Monty Python’s Flying Circus, whose irreverent humour – a blend of satire, surrealism and silliness – helped revolutionise British comedy.
Jones wrote and performed for the troupe’s early-70s TV series and films including Monty Python and the Holy Grail in 1975 and Life of Brian in 1979.
Playing the mother of Brian, a hapless young man who is mistaken for Jesus, he delivered one of the Pythons’ most famous lines: “He’s not the Messiah. He’s a very naughty boy!”
The Life of Brian 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.
His other on-screen, 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 Idle, Palin, and 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.