The 71-year-old comedian describes how he received the diagnosis in a new ITV programme in which he looks at customs and beliefs surrounding death.
He says how the week began with him getting a hearing aid and being prescribed pills for heartburn.
The Scottish star tells the programme: "It was a funny week I had. On the Monday I got hearing aids, on the Tuesday I got pills for heartburn which I have to take all the time.
"And on the Wednesday I got news that I had prostate cancer and Parkinson's disease.
"They told me on the phone, they said, 'Look we've had the result and it's cancer.' And I said, 'Oh nobody's ever said that to me before'."
He told Radio Times magazine: "I remember I went through to the bedroom to answer the phone, and (wife) Pamela (Stephenson) was behind me - I thought she was gonna catch me.
"And she sort of held me, and I went, 'Oh Jesus...' But when we went into the living room I went, phrrhrht."
Connolly has since been given the all-clear after treatment for prostate cancer.
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In the interview, the star dismissed a claim that the drugs that he had to take for Parkinson's caused on-stage memory loss in Belfast last year.
"Oh that was bullshit! It makes me so f****** angry!," he said. "I've lost my train of thought all (through) my career! It's what makes me different from everybody else - 'Where was I, what was I saying?'"
He added: "I just ramble off and come back ages later."
Connolly said that he uses notebooks to improve his memory.
"I've put myself on a strict regime of crossword books. They remind me of everything. I have to train my memory," he said
"I've got a notebook with all the words I tend to forget. It's the same ones cropping up again and again."
According to the NHS, symptoms of Parkinson's disease can vary and the condition affects people in different way.
Possible symptoms can be split between three broad categories (see here for more detail):
- symptoms that affect physical movement – known as motor symptoms
- symptoms that affect mood, thinking and behaviour – known as neuropsychiatric symptoms
- symptoms that affect your autonomic nervous system (the nervous system that controls your 'automatic' functions such as breathing and urination) known as autonomic dysfunction
Connolly talks about his own death in the ITV documentary, Billy Connolly's Big Send Off.
"I don't think I want a resting place. I want to be scattered to the wind," he says.
"Actually, I'd like to think we could have the coffin in a hearse, empty. And the real me being buried somewhere by pals, quietly, with a tree on top of me."
:: The first part of Billy Connolly's Big Send Off airs on May 7th at 9pm on ITV.