The 71-year-old comedian told how an Australian doctor diagnosed him on the spot after seeing him walking through a hotel lobby.
The man approached Connolly and told him to see his doctor right away because his gait suggested he was showing early signs of the illness.
Last September, Connolly announced he had had surgery for prostate cancer and was being treated for early symptoms of Parkinson's, a degenerative brain disorder.
Speaking in detail for the first time about his health battles, Connolly told how he was staying at a hotel in California preparing to appear on Conan O'Brien's television chat show when he met the concerned fan.
He said: "It was the strangest thing. 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 also told how his prostate cancer was diagnosed during a routine examination. He had surgery in America and was given the all-clear in December.
He said: "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.
"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 it never crossed my mind that I might.
"It's that arrogance thing, I think I'm going to live forever."
He said was taking a relaxed approach to his illness and joked he had always suffered from memory loss, a symptom of Parkinson's, during stand-up routines.
He added: "I prefer not to give it any notice.
"I don't see much shaking going on and I have always had a sh**** memory anyway. I have forgotten things my entire career.
"I was taking drugs to control the Parkinson's, but I'm not on them any more. 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.
"In terms of treatment I think some of the stem cell stuff is very promising but they have a lot of problems legally getting it through."
Daiga Heisters, of the charity Parkinson's UK, said walking problems were a tell-tale sign of the illness.
She said: "One of the first things Parkinson's specialists do is make patients walk up and down a corridor.
"People with Parkinson's have a lopsided way of walking, they tend to drag one of their legs. It is so minute, though, that if you didn't know Parkinson's then you wouldn't notice it.
"It is one of the early symptoms and is caused by the depletion of dopamine in the brain, which affects movement."
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.
Last week, he said he would not vote in the independence referendum because he would be in New Zealand when the vote was held.