The actor and comedian was in Glasgow yesterday and broke the news during a television interview.
He was talking about Celtic's Champions League match against Barcelona when he said: "I got the clearance on Wednesday on my cancer so I'm OK."
Last month his spokeswoman said he was diagnosed with early-stage prostate cancer and had minor surgery in America. She also said Connolly "has been assessed as having the initial symptoms of Parkinson's disease, for which he is receiving the appropriate treatment" but will continue to perform on stage and screen.
It was also stated: "Billy has been assured by experts that the findings will in no way inhibit or affect his ability to work."
The 70-year-old started his showbusiness career as a folk singer, developing the stand-up act that made him famous and led to a career in television and film.
He went on to perform sell-out stand-up shows around the world, present a series of documentaries and become an in-demand character actor, starring alongside Judi Dench in Mrs Brown and playing a dwarf warrior in the Hobbit movie.
He is married to New Zealand-born actress and psychologist Pamela Stephenson, whose biography of her husband, simply called Billy, was a best-seller.
After his condition was made public last month Connolly made his first public apperance at a screening of A Single Shot at the Tribeca Film and Cinema Society in New York on September 19. He promised to continue performing despite the surgery. He will appear in The Hobbit: The Desolation Of Smaug later this year before undertaking an theatrical tour of New Zealand in 2014.