Corbett was one of Britain's best-loved entertainers and his partnership with Ronnie Barker in the BBC sketch show was one of the most popular of the 1970s and 1980s.
He was brought up as a Presbyterian and spoke of how faith had been a huge part of his life.
In an interview with the journalist Nigel Farndale he said: "We were very serious church-goers, yes. College Street Church. We used to have a long walk there, every morning, 11 o'clock, then back home for lunch, or probably dinner as it was called then, and off again to the service in the evening."
He explained that he no longer went to church.
His publicist said in a statement he died in hospital "surrounded by his loving family".
It is thought he had been in ill health for some time. His wife of more than 50 years, Anne Hart, said that at a celebration dinner to mark his award of a CBE in the 2012 New Year Honours he collapsed and was rushed to hospital.
Revd Simon Carver is a media commentator and told Premier's News Hour: "He was one of those 'old-fashioned' entertainers that was loved by all ages.
"He made fun of himself and was very happy to poke fun at himself, he was a very inclusive sort of comedian.
"People enjoyed the gentleness of his humour. He lived a long, productive life. We mourn when we lose people, people loved him but he had a long and productive life and there's not much to be sorry for in all of that."
Corbett launched his career at his local church youth club in Edinburgh when he played the Wicked Aunt in a pantomime at the age of 15.
The small screen aside, Corbett's talents also extended to the theatre and big screen.
He starred in a host of theatre productions such as The Seven Year Itch and Out Of Order. A notable film appearance was his stint in John Cleese's 1996 follow-up to A Fish Called Wanda, Fierce Creatures.
He also had roles in big-name titles such as Top Of The Form, You're Only Young Once, Casino Royale, and No Sex Please, We're British.
The Edinburgh-born entertainer also had various solo projects, among them he hosted the BBC One game show Small Talk for two years from 1994 to 1996.
He is survived by his wife Anne and two daughters.
Revd Simon Carver speaking to Premier's Hannah Tooley:
