Jones, who was aged 77, had been suffering from a form of dementia that affected his ability to speak since 2015.
Renowned as a performer and director with Monty Python, Jones was also a prolific screenwriter, novelist, respected medieval historian, and occasional poet.
Sir Michael Palin led the tributes to his late colleague and friend, calling “an enormous enthusiast.”
“He threw himself into things with such passion and such energy and he really refused to take on things which didn’t excite him and which didn’t feel different from what else was around,” Palin said.
“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.”
Fellow Python star John Cleese tweeted, “It feels strange that a man of so many talents and such endless enthusiasm, should have faded so gently away,” adding wryly, “Two down, four to go.”
Eric Idle said that he loved Terry Jones from “the moment I saw him on stage at the Edinburgh Festival in 1963” and recalled the “many laughs, moments of total hilarity onstage and off we have all shared with him.
“It’s too sad if you knew him, but if you didn’t you will always smile at the many wonderfully funny moments he gave us.”
Tim Robbins, who starred in Jones’ 1989 comedy Erik the Viking, called him a “comic genius”.
“A kind, lovely, generous man. And a comic genius who, with the Pythons, defined what comedy could be for my generation. I cherished the time I got to spend with him. Rest In Peace.”
Beatles biographer Mark Lewisohn dubbed losing one of the Pythons as “pretty close to losing one of the Beatles”.
“It’s losing someone important in the way you like life to be. Resounding and eternal applause for Terry Jones,” he wrote.
Author and journalist Jon Ronson asked his followers, “What’s better than being funny and kind?”
“For a person my age Monty Python was like punk and the Beatles and Peter Cook all rolled into one. I never stopped listening to the albums. And on the few occasions I met Terry Jones he was incredibly nice. What's better than being funny and kind?”
Broadcaster Matt Stephens shared an anecdote of his time with Jones near the end of his life, highlighting his friend’s life as “a lucent example of human kindness”.
“I’ll miss Terry Jones, a dear friend and lovely human being. One night, I was sat with him in his lounge, watching ‘Easter Parade’ starring Fred Astaire & Judy Garland. We sat in silence, sipping red wine when, towards the end of the film I cried.
“Terry reached across and took my hand, gently squeezing it. This caused me to cry even more, but he just continued to hold my hand until the end. His ability to talk may have slipped away, but his pure kindness still shone through.
"Terry doesn’t just leave behind a beautiful daughter & wife, son & daughters, the remaining Pythons, millions of fans and an astonishing legacy, he has also left us as a lucent example of human kindness. Rest in peace Terry.”