The 71-year-old star confirmed he had been diagnosed with the illness in September, revealing he had also undergone surgery for prostate cancer.
Billy has now spoken about his health in detail, explaining it was a fan who encouraged him to seek medical help after watching him walking through a hotel lobby.
"It was the strangest thing of all. I was doing Conan O'Brien's thing and they put me up in the Sportsmen's Lodge in Los Angeles. I was walking through the lobby and every time I had gone through there was a crowd of boys and girls and a couple of adults. It turned out they were dancers from Australia. The guy who was in charge of them came over to me one day and said, 'Billy, I'm a big fan, I'm from Tasmania.' He said, 'I'm a surgeon and I have been watching you walking, you have a strange gait'. That was the way he put it," Billy recalled on a US radio show, according to MailOnline.
"He said, 'You're showing distinct signs of early onset Parkinson's disease, see your doctor.' I think it was the way I held myself when I was walking."
Billy followed the advice and, after some blood and other tests, was told he had the illness.
His cancer was discovered during a routine examination. The Scottish comedian had an operation and received the all clear in December.
"It was found by the routine finger up the bum test. When I was told by the doctor I had cancer I said to him, 'I've never been told that before.' Usually you are only told once," he explained.
Before the surgery Billy's doctor reassured him he wouldn't die. The actor was astounded to hear that, revealing the "arrogance thing" meant it hadn't even occurred to him that he might pass away.
Billy isn't letting his diagnosis get him down, insisting he hasn't felt ill yet.
"I prefer not to give it any notice. I don't see much shaking going on and I have always had a [bad] memory anyway," he said.
The star was on medication for a while, but has now stopped taking it. Apparently he was told the side effects he could experience might be worse than the disease's symptoms.
