Palin, who performed with Jones in Monty Python, described Jones as “one of my closest, most valued friends” in a statement to the PA news agency.
“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.
“I feel very fortunate to have shared so much of my life with him and my heart goes out to Anna, Alison and all his family.”
Jones' agent confirmed the comedian's death this morning. A statement from 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 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.”
Stephen Fry paid tribute to Jones on Twitter, writing: “a great foot has come down to stamp on you".
“My god what pleasure you gave, what untrammelled joy and delight. What a wonderful talent, heart and mind.”
Farewell, Terry Jones. The great foot has come down to stamp on you. My god what pleasure you gave, what untrammelled joy and delight. What a wonderful talent, heart and mind— Stephen Fry (@stephenfry)January 22, 2020
Bafta also paid tribute to Jones, sharing a photo of the comedian receiving his Special Award for Outstanding Contribution to Film & Television from Palin at the 2016 Bafta Cymru Awards.
We're saddened to hear of the passing of Terry Jones. Here he is receiving the Special Award For Outstanding Contribution to Film & Television from friend and fellow Python Michael Palin, at the 2016 @BAFTACymru Awards. pic.twitter.com/iQGLTWIQyL— BAFTA (@BAFTA)January 22, 2020
More stars shared their tributes on Twitter, with author David Walliams writing: “Thank you Terry for a lifetime of laughter.”
Thank you Terry for a lifetime of laughter. pic.twitter.com/Z1dqfNklJ9— David Walliams (@davidwalliams)January 22, 2020
John Cleese wrote: "It feels strange that a man of so many talents and such endless enthusiasm, should have faded so gently away."
Just heard about Terry J
It feels strange that a man of so many talents and such endless enthusiasm, should have faded so gently away...
Of his many achievements, for me the greatest gift he gave us all was his direction of 'Life of Brian'. Perfection
Two down, four to go— John Cleese (@JohnCleese)January 22, 2020
Actor and comedian David Schneider described the news as a “punch to the gut”.
“Thanks for making us laugh so much, Terry.”
News that arrives like a punch to the gut. Thanks for making us laugh so much, Terry. https://t.co/v5W9KyO14I— David Schneider (@davidschneider)January 22, 2020
Others that tweeted tributes included Black Mirror writer Charlie Brooker, author Neil Gaiman and screenwriter Simon Blackwell.
RIP the actual genius Terry Jones. Far too many brilliant moments to choose from. Here’s one random wafer-thin mint. https://t.co/qMrR9aOV9s— Charlie Brooker (@charltonbrooker)January 22, 2020
36 years ago I met Terry Jones. I was meant to interview him. I asked for tea, so he opened a bottle of Chablis & got me drunk. He was funny, brilliant and honest. He was irrepressible and is seen here repressing the very young me. Rest in Peace, Terry. You were an inspiration. pic.twitter.com/fNBJZwOFcX— Neil Gaiman (@neilhimself)January 22, 2020
Lovely Terry Jones, the heart of Python. Ripping Yarns remains so gloriously funny, and Bert Fegg's Nasty Book For Boys & Girls made me laugh like a small fool when I was eight. Very sad to see him go.— Simon Blackwell (@simonblackwell)January 22, 2020
A very fond farewell to Terry Jones: Not only 1/6 of the Pythons, Mr Creosote, Arthur Two Sheds Jackson, Dino Vercotti, Mandy Cohen, Prince Herbert, Cardinal Biggles & the Nude Organist, but also esteemed director of all time comedy classic; 'Life Of Brian'. He will be missed. pic.twitter.com/PeBDlvGfsD— edgarwright (@edgarwright)January 22, 2020
You may not have the kind of affection for The Pythons that comedy fans of my vintage have, but know that if you've ever enjoyed any flavour of surreal, silly anti-comedy, you owe them.
And Terry Jones was the beating heart of it all.
What a man.— Rufus Hound 🌨 (@RufusHound)January 22, 2020
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
The influence of Monty Python and reading this book was the catalyst for me applying to drama school, thank you Terry Jones for inspiring so many of us ❤️ pic.twitter.com/TZAsr6L9i2— Nicola Coughlan (@nicolacoughlan)January 22, 2020
Jones' death comes just weeks after the death of Monty Python star Neil Innes, who died on 29 December aged 75.
Jones was an original member of Monty Python, and was responsible for getting them together.
He met writing partner Michael Palin while studying at Oxford University and they went on to write for British comedy shows together.
Jones is survived by his wife Anna, and children Bill, Sally, Siri.