The actor died on Tuesday (January 21) with his wife Anna by his side, his family confirmed.
In 2016, Jones' representatives announced he was diagnosed with frontotemporal dementia leaving him unable to give interviews as the disorder began to affect his ability to communicate.
Jones was also a prolific children’s author and well-respected medieval historian and in 2016 was awarded a Lifetime Achievement award from BAFTA Cymru for his outstanding contribution to TV and film.
A statement from Jones' 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 at the age of 77 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. 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.
“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'.”
After the sad news broke, actor David Schneider tweeted: “News that arrives like a punch to the gut. Thanks for making us laugh so much, Terry.”
Radio presenter Tony Blackburn added: “So sorry to hear Terry Jones has passed away, I just love Monty Python. RIP Terry and thanks for all the laughs.”
So sorry about Terry Jones. Just a very, very, very funny man. And a kind, thoughtful, interesting, and curious one too. What a great body of work he has left though. #TerryJones— Katy Brand (@KatyFBrand)January 22, 2020
Comic Katy Brand tweeted: “So sorry about Terry Jones.
“Just a very, very, very funny man. And a kind, thoughtful, interesting, and curious one too. What a great body of work he has left though. #TerryJones.”
His death comes just weeks after that of Monty Python's Neil Innes, who died on 29 December aged 75.
Last year Terry Gilliam, also a part of Monty Python, confirmed his friend's condition had become so severe he could no longer speak.
Jones was an original member of the legendary comedy troupe, and was responsible for getting them together.
He met his writing partner Michael Palin while studying at Oxford University and they went on to write for British comedy shows together.
The duo went on to create Monty Python's Flying Circus with Palin and Eric Idle as well as Graham Chapman, John Cleese and Terry Gilliam.
The five surviving members, which also included Palin, Idle and Cleese, delighted fans when they reunited for a special live event in 2014,
Jones is survived by his wife Anna, and children Bill, Sally, Siri.