"The operation was a total success, and Billy is fully recovered," his spokeswoman said.
Billy has had a successful stage, TV and film career stretching back five decades
In a statement, she explained that he "recently underwent minor surgery in America after being diagnosed with the very early stages of prostate cancer.
"In addition, Billy has been assessed as having the initial symptoms of Parkinson's disease, for which he is receiving the appropriate treatment."
The 70-year-old actor has been in a number of successful films such as Mrs Brown, in which he appeared alongside Judi Dench, and Dustin Hoffman-produced movie Quartet, as a former opera star who shakes up his retirement home by flirting with staff and pensioners alike.
Starring with Judi Dench in Mrs Brown about Queen Victoria's relationship with her favourite manservant
He began life his working life as welder in the Glasgow shipyards before turning to folk singing and then stand up in the Sixties. His high energy, colourful monologues in which he would stomp about the stage have made him a popular fixture on television.
Earlier this year, he said he wanted to stay young at heart: "Stay young. Me? I'm 37! I haven't changed my attitude to things since I was 37."
In December 2012, Billy received a BAFTA Scotland award for outstanding contribution to showbusiness.
His representative has promised fans that the actor would continue to meet his professional commitments.
She said: "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."
As he tackles his health problems, the actor will rely on the support of his wife Pamela Stephenson, Australian psychologist, who is a former actress herself.
He has been with Pamela Stephenson for over 30 years and they married in 1989
Feisty Pamela has been open about the ups and downs of living with a comedy genius. The couple have been together more than 30 years and have five children - two from his previous marriage and three of their own.
They tied the knot in Fiji in 1989 with him wearing a kilt. Their wedding came after she took custody of his two older children when their mother became unable to care for them and her ultimatum to him to stop drinking or lose her. He has been sober for over 30 years.