Strong was born Marco Giuseppe Salussolia in London to an Italian father and an Austrian mother, and attended Wymondham College in Norfolk. His English name is not a stage name, it was changed by deed poll by his mother when he was a boy to help him fit in with his peers. At school he was the singer in punk rock bands called The Electric Hoax and Private Party. His original ambition was to become a lawyer, but after studying for a year at University in Munich, Germany he decided to change his direction in life and returned home to London. There he enrolled in a joint English and Drama degree at Royal Holloway, and later attended Bristol Old Vic Theatre School.

Strong is a familiar face on British television and has appeared in such drama series as two Prime Suspect serials for ITV: as Inspector (later Detective Chief Superintendent) Larry Hall in Prime Suspect 3 (1993) and Prime Suspect 6 (2003). He also had starring roles in two BBC Two drama serials, Our Friends in the North (1996) and The Long Firm (2004) for which he earned a BAFTA nomination, and also played the villainous Colonel Brand in Sharpe's Mission (1996). He played the romantic lead, Mr. Knightley, in the ITV adaptation of Jane Austen's novel Emma, with Kate Beckinsalein the title role.

In film, one of Strong's most prominent roles was as Steve in the 1997 adaptation of Nick Hornby's Fever Pitch, co-starring opposite Colin Firth and Strong also features in Roman Polanski's 2005 version of Oliver Twist. He played Mussawi in the film Syriana, and in 2005 appeared in Revolver, where he played Sorter, a nerveless, steely assassin "who never misses". In 2006, Strong portrayed the traitorous Wictred in Tristan & Isolde, showing his talent with swordplay. The following year he played Pinbacker in the science-fiction film Sunshine. He had to spend six hours a day in makeup to get Pinbacker's scars. Coincidentally, Strong also appeared in a 1999 film also titled Sunshine.

He got down to the last two considered for the part of Anton Chigurh (Javier Bardem's role) in No Country for Old Men, but despite the persistence of rumours he was never offered the part. In Body of Lies, he played Hani Salaam, head of Jordanian Intelligence. In most of Strong's films he's virtually unrecognizable because he changes his look for each character; in Stardust and Tristan + Isolde, he has long hair, in RocknRolla and The Long Firm he sports a receding hairline, whilst in Body of Lies and Miss Pettigrew Lives for a Day he has a full head of hair). His characters in Low Winter Sun, Heartlands and Fever Pitch however most resemble his true self.

In his theatre career, Strong was nominated in 2003 for the Laurence Olivier Award for Best Performance in a Supporting Role for his role in Shakespeare's Twelfth Night at the Donmar Warehouse in 2002. He is due to film a lead part in the Channel 4 film Endgame (2008).

Since 2006, Strong has provided the narration in the BBC genealogy series Who Do You Think You Are?.