He cancelled a 30-date speaking tour earlier this month after only one appearance due to ill health.
A statement from his family said: “It is with heavy hearts that we bring you such sad news.
“Our dear friend and yours, John Challis, has died peacefully in his sleep, after a long battle with cancer.
“He will always be loved for being ‘Boycie’ and leaves a great legacy of work that will continue to bring pleasure and smiles for many years to come.
“Please respect the privacy of John’s family and friends at this difficult time, and be assured that in the future there will be an occasion to celebrate John’s life – when everyone will be welcome to come along.”
Challis played Terrance Aubrey Boyce in Only Fools And Horses from 1981 to 2003, as well as in Boycie-focused spin-off show The Green Green Grass.
He recently became an honorary citizen of Serbia, where the BBC sitcom remains hugely popular.
Challis made the documentary Boycie In Belgrade, exploring why the show was so beloved in the Balkan country.
Boycie, a cigar-smoking businessman with a mocking laugh, was married to the feisty Marlene – played by Sue Holderness – and regularly butted heads with Sir David’s Del Boy.