The 70-year-old star started his showbusiness career as a folk singer before developing the stand-up act that made him famous.
His spokeswoman said: “Billy Connolly recently underwent minor surgery in America after being diagnosed with the very early stages of prostate cancer. The operation was a total success, and Billy is fully recovered.
“In addition, Billy has been assessed as having the initial symptoms of Parkinson’s disease, for which he is receiving the appropriate treatment.
“Billy has been assured by experts that the findings will in no way inhibit or affect his ability to work, and he will start filming a TV series in the near future, as well as undertaking an extensive theatrical tour of New Zealand in the new year.”
The Glasgow-born star, who began his working life in the Clyde shipyards, became a household name with a string of appearances on Michael Parkinson’s chatshow.
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 with roles including starring alongside Judi Dench in Mrs Brown and playing a dwarf warrior in the forthcoming Hobbit sequels.
Connolly is married to New Zealand-born actress and psychologist Pamela Stephenson, whose biography of her husband, simply called Billy, was a huge best-seller.
He is one of around 127,000 Britons with the disease, which is caused by a loss of brain cells that produce a chemical messenger called dopamine.
Symptoms differ from case to case but often include a tremor or fine shake while the person is at rest, rigidity of muscles, slowness of movement, and unsteady balance.
Other possible symptoms can include memory loss, and earlier this year Connolly admitted he had started to forget his lines during performances.
Speaking about it, he said: “This is fucking terrifying. I feel like I’m going out of my mind.”
There is no cure for Parkinson’s and scientists have been unable to work out why people get the condition.
Connolly was made a CBE in the 2003 Queen’s Birthday Honours and awarded the freedom of his home city in 2010.
Steve Ford, chief executive at Parkinson’s UK, said: “Put simply, Billy Connolly is a much-loved comedy legend and we are sorry to hear that he is being treated for the early symptoms of Parkinson’s. One person every hour will be diagnosed with Parkinson’s in the UK.
Despite this, it remains a little understood condition and we salute Billy’s bravery in speaking out about his condition at this difficult time.
“There are 127,000 people in the UK, like Billy, living with Parkinson’s. Parkinson’s can be a very difficult condition to diagnose, as no two people with Parkinson’s are the same, with symptoms — such a slowness of movement or tremor — changing on a daily, or even hourly, basis.
“Many people, with the right medication, continue to live a full and active life with Parkinson’s, but for some, it can be life-changing and it is vital that Billy gets the support he needs to live with this complex condition.
“We wish Billy and his family all the best as they come to terms with this upsetting diagnosis.”