The 70-year-old Scottish comedian and actor, affectionately known as the Big Yin, underwent surgery in the US after being diagnosed for having the "very early" stages of the cancer, with the operation deemed a "total success".
A spokeswoman for Glasgow-born Connolly, who has fully recovered from the surgery, added that he is receiving treatment after being assessed as having the initial symptoms of Parkinson's disease.
She added: "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."
Connolly is now one of around 127,000 Britons with Parkinson's disease, which is caused by a loss of brain cells that produce a chemical messenger called dopamine.
Symptoms can include a tremor or 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 this, he said: "This is f****** terrifying. I feel like I'm going out of my mind."
Connolly is set to star in the next two episodes of The Hobbit: The Desolation of Smaug and There and Back Again.
He recently appeared in a movie called Quartet and provided his voice for Disney-Pixar's Brave.
Connolly, who is set to start filming a TV series soon and launch a tour of New Zealand next year, "has been assured by experts that the findings will in no way inhibit or affect his ability to work," the statement said.
Yesterday, BBC Scotland broadcast an interview with Connolly by Janice Forsyth, where she talked to him about his favourite music for the series Do The Shuffle. In it, he said he has the "itch" to make more music.
The interview was recorded in February, and Ms Forsyth said: "He was on terrific form, very honest, open and entertaining - an intense, quite emotional experience, actually - and there was no indication that he was ill.
"I drew the session to an end, because I'd run out of steam. He'd arrived early and I'm sure would've continued for another few hours.
"I am sad at the news, but clearly he's been diagnosed early, and that must make a huge difference to the outcome."
Sadie Docherty, the Lord Provost of Glasgow, said in a message to Connolly, said: "I read today of your recent health difficulties and was pleased to learn that you are on the mend following surgery.
"On behalf of the people of Glasgow, who welcomed you so warmly when you were made a Freeman of this city, I send our very best wishes and support to you and your family."
The singer Bob Geldof said his "great friend" would not be deterred by the diagnosis.
He said: "He's helped me lots in my endeavours. He's as strong as an ox mentally from everything he's been through as a kid. So I don't think this will deter him from being that individual that we know."
A spokesman for Connolly's favourite football club, Celtic, said: "Everyone at Celtic would like to pass on our thoughts and best wishes to Billy Connolly."
Steve Ford, chief executive at Parkinson's UK praised Connolly's "bravery" in speaking out about his condition.
He 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.
"We wish Billy and his family all the best as they come to terms with this upsetting diagnosis."
Owen Sharp, chief executive of Prostate Cancer UK, said: "It is always concerning to hear that anyone is faced with prostate cancer, but it is very good news if Billy Connolly's treatment has been successful and we wish him the best in his recovery.
"Prostate cancer is the most common cancer in men, with 250,000 men living with the disease in the UK right now."