He died peacefully at the age of 96 with his family by his side, his agents announced.
He was best known for his appearances in the Last of the Summer Wine and also voicing the character of Wallace in Wallace and Gromit.
He died with his family at his side at Denville Hall - a care home for actors in Northwood, London - on Friday.
Jonathan Altaras Associates released a statement saying: "It is with sadness that we announce that our client Peter Sallis died peacefully, with his family by his side, at Denville Hall on Friday, June 2."
Mr Sallis became a household name in the UK as mild-mannered Norman Clegg in the comedy Last Of The Summer Wine, Britain's longest-running sitcom.
But his role playing loveable inventor Wallace in Nick Park's animated films made his voice known around the world.
Wallace And Gromit scooped two Oscars and Sallis was delighted to have such success late in life.
"It is pleasing knowing millions are going to see your work and enjoy it.
"To still be involved in a project like this at my age is heart-warming," he said.
"To have a legacy like this is very comforting. I am very lucky to have been involved."
Before Wallace, Sallis was synonymous with Last Of The Summer Wine, Britain's longest-running sitcom.
It started life as a Comedy Playhouse pilot in 1972 and became a series in 1973.
Sallis was part of the original cast, playing mild-mannered Norman Clegg.
Other actors came and went but the classic line-up featured Sallis as Cleggy, Bill Owen as Compo and Brian Wilde as Foggy Dewhurst.
The Yorkshire-based sitcom turned the trio, and Kathy Staff, who played Nora Batty, into household names.
When the show began, Sallis already had more than 25 years of acting experience under his belt.
Born in Twickenham, south-west London, his father was a bank manager and his mother was a housewife.
He showed no interest in acting at school and his only link to the stage was his grandmother, who ran a theatrical boarding house in Northampton.
On leaving school he followed his father into a banking career with Barclays and might have stayed there for life were it not for the Second World War.
Sallis signed up for the RAF but failed his aircrew medical and instead became a radio instructor based at RAF Cranwell in Lincolnshire for the duration of the war.
It was at Cranwell that he was asked to appear in a performance of Hay Fever in 1943.
He caught the acting bug and when he was demobbed in 1946 he won a scholarship to Rada.
His first TV role came in 1947, playing Quince in a production of A Midsummer Night's Dream.
In his early career he concentrated on theatre work and appeared opposite Laurence Olivier, John Gielgud and Orson Welles.
During the 1950s and 1960s he worked steadily in a succession of TV shows, with minor parts in episodes of Z Cars, The Avengers and Doctor Who.
His role as Cleggy in Last Of The Summer Wine took up the next three decades.
In 1983, a student, Park, wrote to Sallis asking him to be the voice of a clay character called Wallace.
The actor agreed to do it in exchange for a £50 fee to his favourite charity.
But it was not until 1989 that the first Wallace and Gromit film, A Grand Day Out, finally reached the screen.
The short film was nominated for an Oscar.
Its follow-ups The Wrong Trousers (1993) and A Close Shave (1995) were Oscar winners. Each of the films won a Bafta.
Wallace and Gromit's first feature-length movie, The Curse Of The Were-Rabbit, was released in 2005 and became a box office hit on both sides of the Atlantic.
Park said his creations owed much of their popularity to Sallis.
"Just the way he pronounces Wensleydale cheese is enough. Once he's in place, everyone else fits around him," Park said.
Sallis said he was happy it was his voice, rather than his face, which had become world famous.
"No-one stops me when I speak or when they see me in the street. That's the way I like it," he said.
Sallis married an actress, Elaine Usher, in the 1950s and they had a son, Crispian, before divorcing in 1965.