He was born to working-class parents who showed little affection to their offspring, (as his older sister publicly revealed) in Dagenham, England, and was notably short: 5' 2½" (1.59 m). He was born with a club foot which required extensive hospital treatment and which, coupled with his diminutive stature, made him the butt of jokes by other children. Seeking refuge from his problems, he became a choirboy at the age of six and took up piano and violin. He rapidly developed into a talented pianist and organist and was playing the organ at church weddings by age 14. He attended Dagenham County High School.

While studying music at Oxford University (Magdalen College, where he was an organ scholar), Moore was noticed by Alan Bennett and he recommended him to the producer putting together Beyond the Fringe, a comedy revue which many see as a forerunner to Monty Python's Flying Circus. Beyond the Fringe was at the forefront of the 1960s satire boom. After enormous success in Britain, it transferred to the USA, where it was also a hit.

After following the Establishment Club to New York City, Moore returned to the UK and was offered his own series on the BBC. Not Only... But Also was commissioned as a vehicle for Moore, but when he invited Peter Cook on as a guest, their comedy partnership was so notable that it became a fixture of the series. Cook and Moore are most remembered for their sketches as two working-class men, Pete and Dud, in macs and cloth caps, commenting on politics and the arts, but they fashioned a series of character one-offs, usually with Moore in the role of interviewer to one of Cook's upper-class eccentrics. The pair developed an unorthodox method for scripting the material by using a tape recorder to tape an adlibbed routine that they would then have transcribed and edited. This would not leave enough time to fully rehearse the script so they often had a set of cue cards. Moore was famous for "corpsing" - the programmes often went out live, and Cook would deliberately make him laugh in order to get an even bigger reaction from the studio audience. Regrettably, many of the videotapes of these seminal TV shows were later erased by the BBC, although some of the soundtracks (which were issued on record) have survived.

During his university years Moore became passionately interested in jazz and soon became an accomplished jazz pianist and composer. In the 1960s he formed the acclaimed "Dudley Moore Trio", who performed regularly on British TV, made numerous recordings, and had a long-running residency at Peter Cook's "Establishment Club".

They co-starred in the film Bedazzled (1967) with Eleanor Bron, and also had tours called Behind the Fridge and Good Evening.

However, their three albums of the late 1970s as Derek and Clive, were widely condemned for their use of obscene language. Shortly following the last of these, Ad Nauseum, Moore made a break with Cook, whose alcoholism was affecting his work, to concentrate on his film career. Ironically, when Moore began to manifest the symptoms of the disease that eventually killed him, it was at first suspected that he too had a drinking problem.

In the 1970s, Moore moved to Hollywood, where he appeared in Foul Play (1978) with Goldie Hawn and Chevy Chase. The following year saw his breakout role in Blake Edwards's 10, which he followed up with the movie Wholly Moses. Soon thereafter Arthur (1981), an even bigger hit than 10, which also starred Liza Minnelli and the late Sir John Gielgud (who won an Oscar for his role as Arthur's stern but loving caretaker) and the late Geraldine Fitzgerald (who played his wealthy, socially prominent, but relentless, grandmother who insists on his marrying the daughter of a business associate of the family, and threatens to disinherit him if he doesn't do so).

His subsequent films, including an Arthur sequel and an animated adaptation of King Kong, were inconsistent in terms of both critical and commercial reception. In later years Cook would wind-up Moore by claiming he preferred Arthur 2: On the Rocks to Arthur.

In addition to acting, Moore continued to work as a composer and pianist, composing scores for numerous films and giving piano concerts, which were highlighted by his popular parodies of classical favourites.

Moore was married to actresses Suzy Kendall and Tuesday Weld (by whom he had a son, Patrick, in 1976). His third and fourth wives were Brogan Lane and Nicole Rothschild (one son, Nicholas, born in 1995). Moore dated and was a favorite of some of Hollywood's most attractive women, including the statuesque Susan Anton; he was generally known as Cuddly Dudley.

Moore was deeply affected by the untimely death of Peter Cook in 1995, and for weeks would regularly telephone Cook's home in London just to get the answer phone and hear his friend's voice. Moore attended Cook's memorial service and at the time many people who knew him noted that Moore was behaving strangely and attributed it to grief, drinking or some form of New Age cult.

In September 1999, Moore announced he was suffering from progressive supranuclear palsy, for which there is no treatment. On March 27, 2002, he succumbed to the pneumonia which was a side effect of PSP at the age of 66 in Plainfield, New Jersey.

In June 2001, Dudley Moore was created a Commander of the British Empire (CBE). Despite his deteriorating condition he attended the ceremony at Buckingham Palace to collect his honour.

In December 2004, the Channel 4 television network in the UK broadcast Not Only But Always, a television movie dramatising the relationship between Moore and Cook, although the focus of the production was on Cook. The role of Moore was played by Irish actor Aidan McArdle.