The Welsh actor was one of the six members of Monty Python, starring in films including Life Of Brian and The Meaning Of Life.
His death was confirmed in a family statement, which said he had passed away on the evening of 21 January at his home in north London with his wife Anna Soderstrom by his side.
It said he had been fighting "a long, extremely brave but always good humoured battle with a rare form of dementia".
It was announced that he was suffering from the syndrome in 2016.
He is said to have "gently slipped away" after spending the last few days in the constant company of his wife, children, extended family and many close friends.
The statement went on: "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."
Sir Michael Palin said Jones was a "kind, generous, supportive and passionate about living life to the full".