His long career in showbusiness began when he was aged just 14.
He became Britain’s best-paid TV star, famous for hosting game shows like The Generation Game, Play Your Cards Right and The Price is Right.
A statement from his manager, Ian Wilson, said: “It is with great sadness that the Forsyth family announce that Sir Bruce passed away this afternoon, peacefully at his home surrounded by his wife Wilnelia and all his children.
“A couple of weeks ago, a friend visited him and asked him what he had been doing these last 18 months.
“With a twinkle in his eye, he responded ‘I’ve been very, very busy… being ill!’”
Sir Bruce’s family expressed their thanks to “the many people who have sent cards and letters to Bruce wishing him well over his long illness and know that they will share in part, the great, great loss they feel”.
They said there would be no further comment at the moment and asked for their privacy to be respected “at this most difficult time”.
BBC director general Sir Tony Hall described Sir Bruce as “one of the greatest entertainers our country has ever known”.
“He has delighted millions of people and defined Saturday night television for decades, with shows like the Generation Game and, most recently, Strictly,” he said.
“His warmth and his wit were legendary. I’ve never seen anyone quite like him when it comes to performing in front of a crowd.
“He had a remarkable chemistry with his audience – that’s what made him such an amazing professional and why he was so loved. He has been part of all of our lives, and we’ll miss him dearly.”BBC