Holm was born Ian Holm Cuthbert in Goodmayes, Essex, the son of "relatively elderly" Scottish parents Jean Holm (née Wilson), a nurse, and Dr. James Harvey Cuthbert, a psychiatrist who worked as the superintendent of the West Ham Corporation Mental Hospital and was also a pioneer of electric shock therapy. He had an older brother, Eric. Holm was educated at Chigwell School and then the Royal Academy of Dramatic Art.

Holm was an established star of the Royal Shakespeare Company before making an impact on television and film. In 1965, Holm played Richard III in the BBCs serialisation of the Wars of the Roses plays, based on the RSC production of the plays, and gradually made a name for himself with minor roles in films such as Oh! What a Lovely War (1969), Nicholas and Alexandra (1971), Mary, Queen of Scots (1971) and Young Winston (1972). In 1967, he won a Tony Award for Best Featured Actor in a Play, for playing the role of Lenny in The Homecoming by Harold Pinter.

In 1977, Holm appeared in the TV mini-series Jesus of Nazareth as the Sadducee Zerah, and in the following year played J M Barrie in the BBC TV series The Lost Boys, in which his son Barnaby played the young George Llewelyn Davies.

Holm's first film role to have a major impact was that of the treacherous android, Ash, in Ridley Scott's Alien (1979). His portrayal of Sam Mussabini in Chariots of Fire (1981), earned him a special award at the Cannes Film Festival and an Academy Award nomination for Best Supporting Actor.

Back home in England, he won a BAFTA award, for Best Supporting Actor, for Chariots. In the 1980s, he had memorable roles in Time Bandits (1981), Greystoke - The Legend of Tarzan, Lord of the Apes (1984) and Terry Gilliam's Brazil (1985). He played Lewis Carroll, author of Alice in Wonderland in the Dennis Potter-scripted fantasy Dreamchild (1985).

In 1989 Holm was nominated for a BAFTA award for the TV series Game, Set, and Match. Based on the novels by Len Deighton this tells the story of an intelligence officer (Holm) who discovers that his own wife is an enemy spy.

He continued to perform Shakespeare, and appeared with Kenneth Branagh in Henry V (1989) and as Polonius to Mel Gibson's Hamlet (1990). Holm was reunited with Kenneth Branagh in Mary Shelley's Frankenstein (1994), playing the father of Branagh's Victor Frankenstein.

Holm raised his profile in 1997 with two prominent roles, as the stressed but gentle priest Vito Cornelius in the The Fifth Element and the tormented plaintiff's lawyer in The Sweet Hereafter. Holm was knighted for his services to drama in 1998. In 2001 he starred in From Hell as the physician Sir William Withey Gull.

The same year he appeared as Bilbo Baggins in the blockbuster film The Lord of the Rings: The Fellowship of the Ring, having previously played Bilbo's nephew Frodo Baggins in a 1981 BBC Radio adaptation of The Lord of the Rings. He reappeared in the trilogy in The Lord of the Rings: The Return of the King (2003), for which he shared a SAG award for Outstanding Performance by a Cast in a Motion Picture.

Holm has been nominated for an Emmy Award twice, for a PBS broadcast of a National Theatre production of King Lear, in 1999; and for a supporting role in the HBO film The Last of the Blonde Bombshells opposite Judi Dench, in 2001. Holm has provided voice-overs for many British TV documentaries and commercials.

Holm is a favorite actor of Terry Gilliam, having appeared in Time Bandits and Brazil. Holm has also appeared in two David Cronenberg films, Naked Lunch (1991) and eXistenZ (1999) and is Harold Pinter's favourite actor, the playwright once stating: "He puts on my shoe, and it fits!" Holm made a stir as Lenny in the first ever performance of Pinter's masterpiece The Homecoming.

He has played Napoleon Bonaparte three times. First, in the 1972 television series Napoleon and Love. Next, in a cameo comic rendition, in Terry Gilliam's Time Bandits from 1981. He completed the set in 2001 playing the fallen and exiled leader in the fanciful film The Emperor's New Clothes.