Diagnosed with leukaemia in 2010, the author and critic had movingly written about his terminal illness during the final years of his life, the BBC reported on Thursday.
Born Vivian James in 1939, he moved to England in 1961 and rose to prominence as a literary critic and TV columnist.
He went on to deliver wry commentary on international programming in such shows as Clive James On Television.
The show saw him introduce amusing and off-beat TV clips from around the world, most famously from Japanese game show Endurance.
According to a statement from his agents, he died at home in Cambridge on Sunday. A private funeral was held on Wednesday in the chapel at Pembroke College.
"Clive died almost 10 years after his first terminal diagnosis, and one month after he laid down his pen for the last time," the statement read.
"He endured his ever-multiplying illnesses with patience and good humour, knowing until the last moment that he had experienced more than his fair share of this 'great, good world'.
"He was grateful to the staff at Addenbrooke's Hospital (in Cambridge) for their care and kindness, which unexpectedly allowed him so much extra time.
"His family would like to thank the nurses of the Arthur Rank Hospice at Home team for their help in his last days, which allowed him to die peacefully and at home, surrounded by his family and his books."
Singer Alison Moyet was among many to pay tribute to a man she described as a "bright, beaming boy".
Ex-tabloid editor Piers Morgan remembered him as "a brilliantly funny man", while presenter Gaby Roslin said he had been "incredibly kind".
"We were lucky to have him for so long after his diagnosis," wrote actor Samuel West. "We were lucky to have him at all."
Reverend Richard Coles said he was "the best telly critic that ever there was", while Margarita Pracatan - the Cuban singer James helped make a household name - paid tribute to his "intelligence... talent and beautiful way of living".
Tony Hall, the BBC's director general, said the "irreplaceable" James was "a clever, witty and thought-provoking broadcaster".
"He had a huge range of talents and everything he did was essential listening or viewing," Lord Hall continued.
( With inputs from IANS )