Jones was diagnosed with frontotemporal dementia in 2016.
A statement released by his family said: “We are deeply saddened to have to announce the passing of beloved husband and father, Terry Jones.
“Terry passed away on the evening of 21 January 2020 with his wife Anna Soderstrom by his side after a long, extremely brave but always good-humoured battle with a rare form of dementia, FTD.
“Over the past few days his wife, children, extended family and many close friends have been constantly with Terry as he gently slipped away at his home in north London.
The statement continued: “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.
“His work with Monty Python, his books, films, television programmes, poems and other work will live on forever, a fitting legacy to a true polymath.”
After Jones graduated from Oxford University with Michael Palin in the late 1960s, they co-created Monty Python’s Flying Circus with Cambridge graduates Eric Idle, John Cleese, Graham Chapman and filmmaker Terry Gilliam.
Jones was behind some of the show’s more surreal and ambitious sketches.
He stepped behind the camera alongside Gilliam in 1975 as co-director of Monty Python and the Holy Grail. He took on sole directing responsibilities for the subsequent big-screen productions Life of Brian (1979) and The Meaning of Life (1983).
His most recent film was the 2015 comedy Absolutely Anything, which starred Simon Pegg.
Recalling meeting Jones at Oxford University, Palin said: The first thing that struck me was what a nice bloke he was. He had no airs and graces. We had a similar idea of what humour could do and where it should go, mainly because we both liked characters; we both appreciated that comedy wasn’t just jokes.”
His family said: “We, his wife Anna, children Bill, Sally, Siri and extended family would like to thank Terry’s wonderful medical professionals and carers for making the past few years not only bearable but often joyful.
“We hope that this disease will one day be eradicated entirely. 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’.”
His former co-star, writing partner and friend Michael Palin recently revealed that Jones was “not doing terribly well”.
When asked on BBC Radio 2 how Jones was getting on, he said: “”The kind of dementia he has is not something that can be cured particularly. It’s just a matter of time.
“I go and see him, but he can’t speak much, which is a terrible thing.”
He shared a story about how, during a recent visit, he brought a book they wrote together in the 1980s called Bert Fegg’s Encyclopaedia of All World Knowledge, and was tickled to see that Jones would only laugh at the bits he had written without Palin.
“I thought, ‘That shows that something is ticking over’,” he said.
Following the announcement, Cleese and Palin have paid touching tribute to their co-star.