Irons was born in Cowes, Isle of Wight, the son of Barbara Anne (née Sharpe), a housewife, and Paul Dugan Irons, an accountant. Part of his maternal ancestry is Irish, and his great-grandfather was one of the first Metropolitan Policemen and later a Chartist. Irons also has a brother, Christopher.

He was educated at Sherborne School in Dorset, (c. 1962–1966). He achieved some fame as the drummer and harmonica player (most memorably for his rendition of "Moon River" on harmonica) in a four-man school band called the Four Pillars of Wisdom. They performed, in a classroom normally used as a physics lab, for the entertainment of boys compulsorily exiled from their houses for two hours on Sunday afternoons. He was also known within Abbey House as half of a comic duo performing skits on Halloween and at end-of-term House Suppers.

Irons trained as an actor at the Bristol Old Vic Theatre School and is now president of its fundraising appeal. He performed a number of plays and supported himself by busking on the streets of Bristol, before appearing on the London stage as John the Baptist and Judas opposite David Essex in Godspell, which opened at the Round House on 17 November 1971 before transferring to Wyndham's Theatre playing a total of 1,128 performances.

Irons' film debut came with Nijinsky in 1980. He appeared sporadically in films during the 1980s, including the Cannes Palme d'Or winner The Mission in 1986, and in the dual role of twin physicians in David Cronenberg's Dead Ringers in 1988. Over the years, Irons has become known for playing somber, often mentally tortured characters.

Other films include Danny the Champion of the World (1989), Reversal of Fortune (1990), for which he won the Academy Award for Best Actor, Kafka (1991), Damage (1993), The House of the Spirits (1993) appearing again with Glenn Close and Meryl Streep, Die Hard With a Vengeance (1995), Bernardo Bertolucci's Stealing Beauty (1996), the 1997 remake of Lolita and as the musketeer Aramis opposite Leonardo DiCaprio in the 1998 film version of The Man in the Iron Mask (1998).

He is also known for playing the evil wizard Profion, along with Bruce Payne as Damodor, in the 2000 film, Dungeons and Dragons, from Time Warner studio New Line Cinema. The film was also based on the Tabletop role-playing game, Dungeons and Dragons.

He played the Über-Morlock from the movie The Time Machine (2002). In 2004, Irons played Severus Snape in Comic Relief's Harry Potter parody, "Harry Potter and the Secret Chamberpot of Azerbaijan". Interestingly enough, Irons and Alan Rickman (who plays Snape in the Harry Potter film series), played the Gruber brothers, Simon and Hans, respectively, in the Die Hard film series.

In 2005, he appeared in the films Casanova opposite Heath Ledger, and Ridley Scott's Kingdom of Heaven. He has co-starred with John Malkovich in two movies; The Man in the Iron Mask (1998) and Eragon (2006), though they did not have any scenes together in Eragon.