Harrison was born in Huyton on Merseyside and was educated at Liverpool College. He first appeared on the stage in 1924 in Liverpool. 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 continued to appear in London, in George Bernard Shaw's Heartbreak House, Pirandello's Henry IV, and in 1984 he appeared at the Haymarket Theatre with Claudette Colbert in Frederick Lonsdale's Aren't We All?. He again appeared at the Haymarket in J. M. Barrie's The Admirable Crichton with Edward Fox.

Harrison 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 show made a star of 35 year old Audrey Hepburn, and 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 could not sing, and so the music in both these musicals had to be carefully written. Harrison "spoke" the words to the music, and it sounded, more or less, like singing. Although Harrison's acting was often described as limited, he attracted favourable notices for 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.

Harrison was married six times. In 1942 he divorced his first wife, Colette Thomas, and married actress Lilli Palmer the next year; the two later appeared in numerous plays and films. After several years in film, he achieved wide acclaim starring in the adaptation of Noel Coward's Blithe Spirit (1945). He followed that with his first major American film, starring as King Mongkut in Anna and the King of Siam.

Harrison's affair with young actress Carole Landis, which is suspected to have played some part in her suicide, caused a scandal but failed to derail his career. Harrison and Palmer divorced in 1957. He soon remarried, to actress Kay Kendall. According to Palmer, Harrison requested a divorce to marry Kendall because he knew that she was dying from leukaemia. After Kendall's untimely death, it was rumoured that he tried unsuccessfully to reconcile with Lilli. He was later married to Welsh-born Rachel Roberts, who later, like Landis, committed suicide by taking sleeping pills; to Elizabeth Rees-Williams (the first wife of Irish actor Richard Harris); and to Mercia Tinker, who would become his widow in 1990.

The chronology of Harrison's six marriages is as follows:

Colette Thomas (1934-1942), (one son, the actor/singer Noel Harrison) Lilli Palmer (1943-1957), (one son, the novelist/playwright Carey Harrison) Kay Kendall (1957-1959) Rachel Roberts (1962-1971) Elizabeth Harris (1971-1975), (three stepsons, Damian Harris, Jared Harris and Jamie Harris) Mercia Tinker (1978-1990) On 25 July 1989, he was knighted by Queen Elizabeth II at Buckingham Palace, while an orchestra played the music of songs from My Fair Lady.

Having retired from films in the late 1970s, he had continued to act on Broadway until the very end, despite suffering from glaucoma, painful teeth and a failing memory. In 1990 he was appearing on Broadway in The Circle by W. Somerset Maugham, opposite Glynis Johns, when he fell ill. It was discovered that he had pancreatic cancer but had been unaware of it, and he died peacefully three weeks later in New York City at the age of 82, causing the show to end prematurely.

For his contribution to motion pictures, Rex Harrison has a star on the Hollywood Walk of Fame at 6906 Hollywood Boulevard. and for his contribution to the television industry at 6380 Hollywood Boulevard.