Greengrass was born in Cheam, Surrey. His mother was a teacher and his father a river pilot and merchant seaman. He is the brother of noted English historian Mark Greengrass. Greengrass was educated at Westcourt Primary School and Gravesend Grammar School, Sevenoaks School and Queens' College, Cambridge. He first worked as a director in the 1980s, for the ITV current affairs programme World in Action; his investigation of timber-framed house construction has been cited as preventing its widespread adoption in England . At the same time he co-authored the notorious book Spycatcher with Peter Wright, former assistant director of MI5, which contained enough sensitive information that the British Government made an unsuccessful attempt to ban it.He then moved into drama, directing made-for-television films such as The One That Got Away, based on Chris Ryan's book about SAS actions in the Gulf War, and The Fix, based on the story of the betting scandal which shook British football in 1964.

His 1998 film The Theory of Flight starred Kenneth Branagh and Helena Bonham Carter, who played a woman with motor neurone disease. The film dealt with the difficult issue of the sexuality of people with disabilities.

Greengrass co-wrote the screenplay for Omagh, which depicted the 1998 bombing of Omagh, and directed The Murder of Stephen Lawrence (1999), which told the story of Stephen Lawrence, a black youth whose murder was not properly investigated by the Metropolitan Police and his mother's investigations, which led to accusations about institutional racism in the police.

Bloody Sunday (2002), depicted the 1972 Bloody Sunday shootings of Northern Irish anti-internment activists by British soldiers in an almost documentary style; it shared First Prize at the 2002 Berlin Film Festival with Hayao Miyazaki's Spirited Away.

Based on that film, Greengrass was hired to direct 2004's The Bourne Supremacy, a sequel to the 2002 film The Bourne Identity, after the first film's director, Doug Liman left the project. The film starred Matt Damon as Jason Bourne, an amnesiac who realizes he was once a top CIA assassin and is now being pursued by his former employers. It proved to be an unexpectedly enormous financial and critical success, and secured Greengrass's reputation and ability to get his smaller, more personal films made.

In 2006, Greengrass directed United 93, a film based on the September 11th hijacking of United Airlines Flight 93. The film received immense critical acclaim, particularly for Greengrass' again quasi-documentary-style directing. After receiving many Best Director awards and nominations from critics circles (including the Broadcast Film Critics Association), Greengrass won the BAFTA award for Best Director at the 60th British Academy Film Awards and received an Oscar nomination for Achievement in Directing at the 79th Academy Awards. For his role in writing the film, he earned Writers Guild of America Award and BAFTA nominations for Best Original Screenplay.

He followed this with a return to the Bourne franchise. The Bourne Ultimatum, released in 2007, was an even bigger success than the previous two films and provided him with yet another BAFTA nomination for Best Director at the 61st British Academy Film Awards.

He directed Green Zone, a film of Imperial Life in the Emerald City, the bestselling, award-winning book by the Washington Post's Baghdad bureau chief, Rajiv Chandrasekaran. It details alleged mistakes made in post-war Iraq. It was filmed in Spain and Morocco with Matt Damon and Greg Kinnear and released in 2010.

Greengrass was initially attached to direct Watchmen, but the production was shut down a few weeks before filming was due to start and the Watchmen film was directed by Zack Snyder instead.

Greengrass's future plans include directing They Marched into Sunlight, a book by David Maraniss which revolves around the controversy surrounding the Vietnam conflict, focusing on one day, when a major battle was occurring in Vietnam and a major protest was simultaneously happening in the US. Also, it was announced that Greengrass is expected to be named the director of a remake of the 1966 film Fantastic Voyage.[1]

Greengrass currently lives in Highmoor, Henley-on-Thames, England