His son Steve Finan O'Connor said he was a "unique comedian who was light years ahead of political correctness".
O'Connor rose to fame on TV show Opportunity Knocks, which he won three times.
He went on to star in The Comedians and host shows including Name That Tune, Crosswits and the Tom O'Connor Show.
He leaves a wife and four children, as well as 16 grandchildren and a great-granddaughter.
His son added: "Tom was famously known for a brand of humour that was 100% clean and always totally family friendly."
He said his father, who was also an actor, was a "firm TV favourite".
O'Connor was born in Bootle, Merseyside, and went on to become a maths teacher and assistant headteacher.
He started his showbusiness career as a singer, before introducing comedy into his act - he was still teaching during the day, and performing on the club circuit at night.
He became a professional entertainer in 1972, establishing himself as a household name with shows like Pick Pockets and The Zodiac Game.
He hosted Name That Tune from 1976 until 1983.
His career also saw him appearing at the Royal Variety Show at the London Palladium and being the subject of This Is Your Life.
As well as hosting quiz shows - which also included I've Got a Secret and Gambit - he was also an actor, starring as Father Tom in daytime soap Doctors in the early 2000s. He won the celebrity edition of Come Dine With Me in 2010 and competed on the Pointless Celebrities quiz show with his daughter-in-law, Olympic gold medallist Denise Lewis, the following year.
O'Connor also made appearances as a guest in Countdown's dictionary corner and received an award from the Channel 4 quiz for being the first to mark 100 appearances on the show.
In a video on his website, O'Connor said: "When I grew up as a kid in wartime Merseyside, I never dreamed I'd have a career that started as a schoolteacher, went to folk singer, then country and western singer, stand-up talker and TV presenter. I've been lucky."
Denise Lewis said she had watched his TV shows with her mother on Saturday nights and when she first met him, was overwhelmed at how sweet, genuine and kind he was.
"It was exactly the person we saw on TV day and night," she added.
TV presenter Piers Morgan was among those to pay tribute to O'Connor, calling him a "Liverpool legend and a very funny man".
"Sad news. Thanks for all the laughs, Tom," he said on Twitter.
BBC Breakfast host Dan Walker tweeted that O'Connor was "kind, funny and a true gent".
Liverpool City Council said: "Sad news breaking about the death of veteran Liverpool comedian Tom O'Connor. Our thoughts are with his family and friends."