Born René Cadier, Chesney died on the 12th April at Kingston Hospital.
Morris Bright, the Chairman of Elstree Studios, posted on Twitter: "Sad to hear famed sitcom writer Ronald Chesney has died aged 98. One half of the writing team behind such shows as The Rag Trade, Meet The Wife and On The Buses he was also in his younger days Britain's most famous and successful harmonica player. Lovely modest chap too."
Born in 1920, Chesney left school at 16 to become a professional harmonica player and during World War II was enlisted to entertain troops at bases around the world.
It was when appearing on the show Educating Archie that Chesney met Wolfe, who was a scriptwriter on the ventriloquism show. Wolfe was signed up as a scriptwriter on the series in 1955 and the duo began working together.
Their first TV hit was The Rag Trade in 1961, an ensemble sitcom starring Peter Jones, Sheila Hancock, Barbara Windsor and Reg Varney which centred on a small clothing workshop. Running for three series on the BBC, sustained popularity saw it revived for a further two series in the late 1970s by LWT. A South African adaptation of the comedy was being made as recently as 2003.
Meet The Wife, a sitcom starring Freddie Frinton and Thora Hird, followed its success in 1963. The series entered international consciousness when name-checked by The Beatles in Good Morning Good Morning.
Romany Jones, a sitcom about families living on a caravan site starring Arthur Mullard, Queenie Watts and James Beck ran for four series from 1972, and span-off into Yus, My Dear, lasting a further two series.
The duo's other collaborations include Buses spin-off Don't Drink The Water; the short-lived John Inman sitcom Take A Letter Mr. Jones...; and Rag Trade-inspired period comedy Wild, Wild Women. They also wrote for 'Allo 'Allo!, and penned the three On The Buses films, all box office hits.
Chesney, who was married with two children, continued to play the harmonica into the 2000s and was the President of the National Harmonica League.