A statement released by his family said: "Iconic television host and broadcaster Bob Holness passed away peacefully in his sleep during the early hours of the morning, aged 83, after his health deteriorated following a number of minor strokes over the past few years.
"Although Bob will be best remembered for being the host of the cult television programme Blockbusters, it should be mentioned Bob was also an accomplished theatre actor and his radio broadcasting career spanned over six decades.
"The famous Pinner resident was beloved by students everywhere for his catchphrase 'I'll have a P, please, Bob'.
Holness leaves his wife Mary, three children and seven grandchildren.
Holness was born in Natal, South Africa, but grew up in Kent after his family moved back to England.
He returned to South Africa as a young man to begin a career as an actor and broadcaster that saw him star in radio plays, including one where he played an early version of superspy James Bond.
In a 2008 interview, he told the BBC: "Well, that just came up through a hole in the floor. I was doing lots of radio plays at the time but I wanted to do something a bit different so when James Bond came up I ventured in and said yes. I had never even heard of him at the time but it became an amazing part to play and the response from listeners was terrific."
He returned to England in 1961 and became a familiar face on television, but it was roles as chairman of BBC 1's Call My Bluff and host of Blockbusters that made him a household name.
The quiz, which ended in 1993, featured student contestants answering a series of trivia questions based on the letters of the alphabet.
A regular feature of the show saw Holness trying to keep a straight face despite facing sniggering students asking him: "Can I have a P please Bob?" - a question he claimed never to be fed up with hearing.
A great presenter, will be sadly missed