Dunn - whose famous catchphrases included "Don't panic, don't panic" and "They don't like it up 'em" - became a recording star in 1971 when his record, Grandad, reached number one.
Born in London in January 1920, Dunn studied at the Italia Conti Academy of Theatre Arts.
He made his first foray into acting in the 1930s, appearing alongside Will Hay in Boys Will Be Boys in 1935 and Good Morning Boys in 1937.
His acting career was interrupted by World War II. He served in Greece before being captured and spending four years as a prisoner of war above a hairdresser's shop in Austria.
The actor would later say that Dad's Army, which ran from 1968 to 1977, was his revenge on his former captors.
The much-loved show featured the exploits of a Home Guard platoon formed to protect the seaside village of Walmington-on-Sea from possible German attack during World War II.
His character ‘Jonesy’, a World War I veteran, was notorious for his often rambling recollections of his time in the Army.
Dunn entitled his 1986 autobiography “Permission To Speak” after another one of his Dad's Army catchphrases.
As well as Dad's Army, Dunn also appeared in such TV shows as Bootsie and Snudge, My Old Man and Grandad.
His last screen credit came playing the Shakespearean clown Verges in a 1984 TV version of Much Ado About Nothing.
He spent his last three decades in Portugal, where he occupied himself with charity work, and as a notable artist painting portraits, landscapes and seascapes until his sight failed.
Dunn, who was awarded an OBE in 1975, spent much of his acting life playing characters older than himself.
Clive Dunn is survived by his wife Priscilla Morgan and their two daughters, Jessica and Polly.