The comedian said he was intimidated at first when he had to star alongside some of the country’s greatest actors.
However, he got over his fear after leaning on the former James Bond star for advice.
The Big Yin said Sir Sean’s help led to his acclaimed performance in Mrs Brown with Dame Judi Dench.
He considers his role as John Brown in the 1997 film about Queen Victoria’s close bond with her Highland ghillie to be the best part he has played during his career.
He said: “My favourite was Mrs Brown with Judi Dench. It was lovely.
“I have acted with some of the greatest English actresses, like Judi Dench and Maggie Smith.
“My acting life has been brilliant.
“On the first day of rehearsals I felt intimidated. They are such professionals but they are such nice people.
“They make you a better actor. Judi can’t act with you and say something to you and you answer by throwing your arms around and shrugging your shoulders and all those things you see on soaps.
“You have to act in response to what you’ve been given and it makes you better. They just drag you into it. You have to stand still, don’t fiddle about and fart about. Less is more. Sean Connery told me that. He said, ‘Do nothing’.
“He said, ‘I loved you in Mrs Brown, you stood there and did nothing’.
“When I was standing with my horse I wouldn’t move. She kept looking out the window and I was still there.”
Speaking on the Adam Buxton podcast, he added: “It is that stillness that’s so powerful. It was just brilliant.
“As you do more than one take you get more used to it and just get on with it.”
Sir Billy, 77, who is suffering from Parkinson’s disease, announced his retirement from stand-up comedy last year and has not acted since his role in the 2016 comedy film, Wild Oats.
However, he has continued to present television documentaries including the recent Billy Connolly’s Great American Trail on ITV.
Sir Billy and Sir Sean, 89, have been close friends for many years and the comic previously said he likes being called “boy” by the Oscar winner despite his advancing years.
He said: “I love him because he calls me ‘boy’. He phones me from time to time when he’s coming to New York and says, ‘We must go for dinner, OK, see you later boy’.”