The Scots comic told how an Australian doctor diagnosed him on the spot after seeing him walking through a hotel lobby.
The man approached 71-year-old Connolly and told him to see his doctor right away as his gait suggested he was showing early signs of the illness.
Last September Connolly announced that he had undergone surgery for prostate cancer and was being treated for early symptoms of Parkinson’s, the degenerative brain disorder.
Speaking in detail for the first time about his health concerns, Connolly insisted that he never considered he might not survive.
He said he was staying at a hotel in Los Angeles preparing to appear on a chat show when he met the concerned fan.
In a US radio interview, Connolly said: “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.
“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.
“Then they did blood tests and various other little bits and pieces and told me I had it.”
Connolly added that his prostate cancer was diagnosed during a routine examination.
He had surgery in America and was given the all-clear in December.
He said: “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. The doctor in the hospital, the one who operated on me, said to me, ‘the good news is you’re not going to die’.
“I said that it never crossed my mind that I might.
“It’s that arrogance thing, I think I’m going to live forever.”
The Glaswegian comic said he was taking a relaxed approach to his illness and joked that he had always suffered from memory loss, a symptom of Parkinson’s, during stand-up routines.
He went on: “The doctor said the side effects were stronger than the effects. I never noticed any side effects but he told me they could include a deep interest in sex and gambling.”
The charity Parkinson’s UK said that Connolly’s condition can manifest itself in general problems with walking, including the dragging of a foot, but that diagnosis was usually more complex.
Chief executive Steve Ford told The Scotsman: “Billy Connolly was fortunate that someone who knew about Parkinson’s picked up on one of its more prominent symptoms in this unusual way. But Billy is a very rare case – diagnosing Parkinson’s is often a lot trickier.
“The early symptoms of Parkinson’s, such as problems with walking or balancing, tremor, or moving more slowly, can all too often be dismissed in isolation, meaning people will wait before seeking medical advice.”
He added: “It is important that people are aware of the possible early stage symptoms of Parkinson’s, so they can avoid any surprise revelations and catch the condition as soon as it begins to develop. We certainly wouldn’t want anyone who thinks that they too may have ‘a strange walk’ to also assume that they will have Parkinson’s, but it is important to see your GP if you are concerned.”
Connolly is due to return to the stage next month when he plays five gigs in America before undertaking a tour of New Zealand in April and May.