Harrison was born in Huyton, then part of Lancashire, and educated at Liverpool College. He first appeared on the stage in 1924 in Liverpool. Harrison's acting career was interrupted during World War II whilst he served in the Royal Air Force, reaching the rank of Flight Lieutenant.

He acted in various stage productions until 11 May 1990. He acted in the West End of London when he was young, appearing in the Terence Rattigan play French Without Tears, which proved to be his breakthrough role.

He alternated appearances in London and New York, winning a Tony Award for his appearance as Henry VIII in Anne of the Thousand Days and international superstardom (and a second Tony Award) for his Henry Higgins in the musical My Fair Lady.

Later appearances included 's Pirandello's Enrico IV, a 1984 appearance at the Haymarket Theatre with Claudette Colbert in Frederick Lonsdale's Aren't We All?, and also on Broadway at the Brooks Atkinson Theatre presented by Douglas Urbanski, at the Haymarket in J. M. Barrie's The Admirable Crichton with Edward Fox. He revived his Henry Higgins in a highly paid revival of My Fair Lady in 1981, cementing his association with the plays of George Bernard Shaw which included a Tony nominated performance as Shotover in Heartbreak House, Julius Caesar in Caesar and Cleopatra, and General Burgoyne in a Los Angeles production of The Devil's Disciple...

Harrison's film debut was in The Great Game (1930), and other notable early films include The Citadel (1938), Night Train to Munich (1940), Major Barbara (1941), Blithe Spirit (1945), Anna and the King of Siam (1946), The Ghost and Mrs. Muir (1947), and The Foxes of Harrow (1947).

He was best known for his portrayal of Professor Henry Higgins in the musical My Fair Lady, based on the George Bernard Shaw play Pygmalion, especially after he reprised the role in the 1964 film version, for which he won a Best Actor Oscar.

The 1956 cast album set sales records at the time. He revived the role on stage in the early 1980s. He also starred in 1967's Doctor Dolittle. Harrison was not by general terms a singer; thus, the music was generally written to allow for long periods of recitative, generally identified as "speaking to the music".

Although excelling in High Comedy (Noel Coward said "Rex Harrison is the greatest interpreter of high comedy in the world... next to Me!"), he attracted favourable notices in dramatic roles such as his portrayal of Julius Caesar in Cleopatra (1963) and as Pope Julius II in The Agony and the Ecstasy (1965), opposite Charlton Heston as Michelangelo.

He also appeared as an aging homosexual man opposite Richard Burton as his lover in Staircase. He also acted in a Hindi movie Shalimar alongside the Indian Superstar Dharmendra.