Along with his writing partner Ronnie Chesney, Wolfe created much-loved catchphrases such as "I'll get you, Butler" in the series set in a London bus depot.
Chesney - whose partnership led to the duo being known as the "the other Two Ronnies" - said it was "like losing my brother".
The pair worked with some of Britain's most popular comic actors over the years, including Kenneth Williams, Barbara Windsor, Beryl Reid, Dame Thora Hird and Benny Hill.
But Wolfe will be best remembered for the saucy comedy On The Buses and The Rag Trade, starring Miriam Karlin, who also died in June.
The writer died yesterday as a result of banging his head on Thursday after falling down stairs at a respite home in London.
His son-in-law Arif Hussein, married to Mr Wolfe's daughter Kathryn, said he was a "wonderful" man.
"He was the kind of father-in-law most people dream about, absolutely.
"Most people talk about their in-laws as people who are interfering, but to me my in-laws were a dream. Ronnie was, from day one, he was absolutely wonderful."
On The Buses was commissioned by ITV after being rejected by the BBC, despite the success of the writer's earlier show The Rag Trade. They created unforgettable characters such as Reg Varney's bus driver Stan Butler, Blakey the fist-shaking inspector, and romeo conductor Jack Harper.
The success also led to spin-off films.
Wolfe had been a radio engineer, then moved into scriptwriting in the 1950s, when he and Chesney created the ventriloquism comedy series Educating Archie.
In 1961 they launched BBC series The Rag Trade - later revived 16 years later by ITV - featuring the well-worn catchphrase "Everybody out!" from bolshy shop steward Karlin.
Other popular shows included Meet The Wife with Dame Thora and Don't Drink The Water, which featured Blakey, played by Stephen Lewis. Less celebrated shows included Yus, My Dear starring Arthur Mullard and Take A Letter Mr Jones, with John Inman.
Paying tribute to his partner, Mr Chesney said: "We were together 50 years - it's like losing my brother."
Wolfe's family also spoke warmly of the grandfather of four's life. His wife Rose said it had been an "unexpectedly sad end for a guy who was so funny in life".
"He was the most incredible husband and we had 58 years of superb marriage harmony," she said.
"I acted as his secretary and PA and typed and computed for him, doing all the work he ever put out."
Wolfe had two daughters, Debbie, 52, and Kathryn, 55, a university lecturer.
Kathryn said: "My fondest memories of my dad are that he was the funniest, most generous person I could have wished to have.
"He was funny in public, with the huge legacy left behind, and funny in private.
"We are going through boxes of funny letters he wrote to me as a child.
"I couldn't have wished to have a better father."