He died peacefully in the hospital, PA Media reported citing a family statement.
Gambon began his acting on the stage in the early 1960s and later moved into TV and film. Notable film roles include a psychotic mob leader in Peter Greenaway's "The Cook, the Thief, His Wife & Her Lover" in 1989 and the elderly King George V in Tom Hooper's "The King's Speech" in 2010.
But his best-known role was as Dumbledore in the "Harry Potter" franchise, a role he took over from the third instalment in the eight-movie series after he replaced the late Richard Harris in 2004.
Gambon was a winner of four BAFTAs, three Olivier Awards and two ensemble cast Screen Actors Guild Awards.
He retired from the stage in 2015 after suffering long-term memory problems but continued to act onscreen until 2019.
Gambon married Anne Miller in 1962, and the couple had a son. While they never divorced, in later years he also had another partner, set designer Philippa Hart, 25 years his junior, with whom he had two children.
Reuters