Figgis was born in Carlisle and grew up in Africa. His early interest was in music and he played keyboards for Bryan Ferry's first band. After working in theatre (he was a musician and performer in the experimental group The People Show) he made his feature film debut with the low budget Stormy Monday in 1988. The film earned him attention as a Director who could get interesting performances from established Hollywood actors. He initially made a splash in America in the 1990s with the gritty thriller Internal Affairs that helped to revive the career of Richard Gere. His next Hollywood feature Mr. Jones was misunderstood by the studio who attempted to market the downbeat story as a feelgood movie resulting in a box office flop. Figgis poured his disenchantment with the film industry into Leaving Las Vegas, creating star turns for Nicholas Cage and Elisabeth Shue which earned Figgis Academy Award nominations for Best Directing and Best Screenplay.

Forays into digital video technology led him to conceive of and direct Timecode, which took advantage of the technology to create an ensemble film shot simultaneously with four cameras all in one take and also presented simultaneously and uncut, dividing the screen into four quarters. Since then, his work output has almost exclusively been on the cutting edge of creative digital filmmaking, with the exception of star-laden Cold Creek Manor. He returned to the Timecode quad-screen approach for his section of Ten Minutes Older, but has also worked on documentary pieces including a segment of Red, White, and Blues and a short piece on the flamenco. His curiosity with the cinematic use of time has led him to cite Robert Enrico's film version of An Occurrence at Owl Creek Bridge as an influential film for him. Figgis has a well-documented love-hate relationship with the Hollywood system which leads him to often be an outspoken critic of the system while also despairing the lack of a better alternative, in his mind, at the moment; at an appearance at Camerimage in 2005, he expressed the view that filmmaking had become "boring and perhaps need[ed] to become even worse before anything better can emerge" successfully at least in reaction. His fascination with camera technology has also led him to create a camera stabilization rig for smaller video cameras, called the Fig Rig which places the camera on a platform held within a steering wheel-like system and has since been released by Manfrotto.

Figgis for several years had a relationship with the actress Saffron Burrows and cast her in several films.