Miller was born in Kingston upon Thames, South West London, England, the son of Anne (née Lee), who worked in theatre production, and Alan Miller, a stage actor and later a stage manager at the BBC. Miller's maternal grandfather was Bernard Lee, famous for playing the character M in the earlier James Bond films.

Miller has stated that he has fond memories of being at Television Centre with his sister and watching Top Of The Pops and Blue Peter being made. Miller was educated at Tiffin School in Kingston upon Thames where he gained his first acting experience and played in the Tiffin Swing Band. Miller left school, aged 17, to pursue his acting career.

After a stint in EastEnders as Jonathan Hewitt, Miller got his big break in films with Hackers (1995), co-starring Angelina Jolie. In 1997, Miller was involved with the creation and operation of Natural Nylon along with friends Jude Law (whom he met in the National Youth Music Theatre), Sadie Frost, Ewan McGregor, Sean Pertwee, Damon Bryant and Bradley Adams.

Natural Nylon folded in 2003. Aside from EastEnders he has appeared on television in the BBC's modernisation of The Canterbury Tales as Artie in The Pardoner's Tale and as Lord Byron in a BBC production about the life of the poet. He worked on the US television series Smith (CBS, Fall 2006). His first appearance on US Television was the 1996 miniseries Dead Man's Walk.

Shortly after Hackers, Miller was cast in Trainspotting (1996), which brought him renown. He was suggested for the role of Sick Boy by Ewan McGregor. The accent he used in the film was so convincing that it led many people to erroneously believe he was Scottish.

In 1997, he played Billy Prior in the film adaptation of Pat Barker's World War I novel, Regeneration, and in 2000 he played the role of Cameron Colley in Complicity (video title Retribution), based on the book by Iain Banks. Also in 2000, he appeared as Simon Sheppard in Wes Craven's Dracula 2000.

In 2005, he was considered for the role of James Bond, replacing Irish actor Pierce Brosnan. The role went to fellow British actor, Daniel Craig. The following year, Miller portrayed cyclist Graeme Obree in The Flying Scotsman.

In 2007, Miller was chosen to play the lead role in a new series for the American network ABC, called Eli Stone. He plays the lead character, a lawyer who struggles with the belief others have that he might be a prophet.