He was best-known for his portrayal of unscrupulous second-hand car dealer Boycie in the beloved sitcom, alongside Sir David Jason and Nicholas Lyndhurst.
Earlier this month, he cancelled a 30-date speaking tour 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.
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"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 an instantly recognisable mocking laugh, was married to the feisty Marlene – played by Sue Holderness – and regularly butted heads with Sir David’s Del Boy.
Paying tribute to her co-star and "beloved friend", Sue Holderness said: "Marlene without Boycie – it’s unthinkable. John Challis was my partner on screen and stage for 36 years and my beloved friend. R.I.P. darling John. I will miss you every day."
Challis was also known for playing Monty Staines in ITV sitcom Benidorm.
His family have requested that instead of flowers, donations are made to his favoured animal charities – Cuan Wildlife Rescue, Tusk and The British Hedgehog Preservation Society.