Michelle Bega, a publicist for Moore, said the star of "Arthur" and "10" died at 11 a.m. EST of pneumonia as a complication of progressive supranuclear palsy, with which he was diagnosed in 1997.
Moore was surrounded by friends, his nurse and medical aides at the time of his passing, Bega said.
"His humor, his joy and his passion to make people laugh will be sorely and deeply missed," said Moore's long-time agent and friend, Lou Pitt.
Moore began his entertainment career in his native England in 1960, when he joined Peter Cook in the cast of the sketch-comedy review "Beyond the Fringe." Moore and Cook -- who died in 1995 -- subsequently worked together on several other projects, including the 1965 BBC comedy series "Not Only ... But Also."
"Fringe," which also featured Alan Bennett and Jonathon Miller in the cast, was presented on the British Broadcasting Corp. in 1964, and eventually enjoyed a two-year run in London's West End.
The show played on Broadway in 1973, earning Cook and Moore a special Tony award for their "unique contribution to the theater of comedy."
Cook and Moore were featured in the 1966 dark comedy "The Wrong Box," starring Michael Caine and John Mills, then teamed up with director Stanley Donen in 1967 for the Faustian comedy "Bedazzled," written by Cook from a story the partners hatched together.
Moore composed the music for "Bedazzled," and for the 1968 romantic comedy "30 Is a Dangerous Age," which he also wrote and starred in. He also composed the musical scores for "Staircase" (1969) and "Inadmissible Evidence" (1968).
He composed the music for "Six Weeks," a 1982 drama in which he co-starred with Mary Tyler Moore," and "The Hound of the Baskervilles," a 1978 send-up of the Sherlock Holmes mythology in which he played Dr. Watson to Cook's Holmes.
In Hollywood, Moore made the most of a featured role as an orchestra conductor in the 1978 Chevy Chase-Goldie Hawn comedy "Foul Play," and became an international star the following year in the sex-comedy "10."
Playing opposite writer-director Blake Edwards' wife, Julie Andrews, Moore stood out as George Webber, a songwriter who survives a midlife crisis set off by an encounter with an impossibly beautiful younger woman, played by Bo Derek in a star-making role of her own.
In 1981, Moore was nominated for an Oscar and a Golden Globe for best actor, for his performance in the title role of "Arthur," as a fabulously wealthy, but personally troubled, alcoholic. John Gielgud won the supporting actor Oscar for his performance as Moore's valet.
In 1993, Moore starred in the CBS-TV comedy "Dudley," as a composer and nightclub pianist who could not commit to personal relationships. The following season, he starred as the single father of three daughters in "Daddy's Girl," also on CBS.
Last year, Moore was honored by Queen Elizabeth with the Commander of the British Empire, one of the United Kingdom's top honors for service in entertainment. He attended the ceremony at Buckingham Palace.
Also last year, he hosted a gala birthday concert at Carnegie Hall to raise money for Dudley Moore Research Fund for Progressive Supranuclear Palsy, which he established as a fund-raising effort for research into the disease that cut short his career.
Moore is survived by his sister Barbara Stevens and his two sons, Patrick and Nicholas. Funeral services and a memorial service are being planned.