The 78-year-old comedian, known affectionately as The Big Yin, was diagnosed with Parkinson’s disease in 2013 and announced his decision to retire from live performance five years later.
Following the airing of ITV’s doc It’s Been A Pleasure on Monday, many of the Scottish star’s close friends – including Sir Paul McCartney and Whoopi Goldberg – paid tribute to his five decades on stage.
A tearful Sheridan Smith, who welcomed her first son Billy in May, revealed she had named him after the comic.
She said: “I named my son after Billy. Did you know that? I’m going to cry.”
Hollywood star Dustin Hoffman, who directed Sir Billy in the 2012 film Quartet, held back tears as he said: “I want him to be around for a long, long time.”
And Sir Elton described him as “the first rock star of comedy”.
The programme also prompted many fans to wish Sir Billy a “happy retirement” on Twitter.
Glaswegian Sir Billy is famous for his energetic presence on stage, and the programme featured footage from across his career.
Symptoms of Parkinson’s disease include decreased mobility and difficulty speaking, leaving him unable to perform as he had in his heyday.
Speaking from his home in Florida, Sir Billy explained his decision to give up performing.
He said: “I have done my stand-up, I did it for 50 years, I did it quite well and it is time to stop.
“My illness, my Parkinson’s disease, has rendered me different. It would either mean renewing what I do and doing something else, or give up what I did and that’s what I’ve done.
“Why do I like to make people laugh? Because it is a jolly thing, it is good for you and it is good for them.
“It is a dynamite thing to be able to do, to get a laugh out of someone.”
He added: “Since the Parkinson’s I’m still the same in many ways, but I don’t think as sharply as I need to to be a stand-up.
“I’ve done 50 years and that’s plenty. Quitting is the right thing to do.”