Marber was born and raised in Wimbledon, London, the son of Brian Marber, a leading and highly regarded technical analyst. He was educated at Rokeby School, St Paul's School, Cranleigh School, and Wadham College, Oxford.
After working for a few years as a stand-up comedian, Marber was a writer and cast member on the radio shows On the Hour and Knowing Me, Knowing You, and their television spinoffs The Day Today and Knowing Me, Knowing You... with Alan Partridge.
Amongst other roles, Marber portrayed the hapless reporter Peter O'Hanraha-hanrahan in both On the Hour and The Day Today, and was involved in a dispute with the comedians Stewart Lee and Richard Herring, who had written for On the Hour, about who had invented the character. Lee and Herring's TV show Fist of Fun would later make several references to their feud with Marber, calling him a "Cornish playwright" and "Cornish curmudgeon". In Stewart Lee's 2010 book, How I Escaped My Certain Fate, Marber is referred to as a "new Shakespeare". Marber reunited with the Knowing Me, Knowing You team in 2003 to record commentaries for the DVD release of the show. He also contributed some new in-character audio material to the DVD release of The Day Today in 2004.
He co-writes Bunk Bed, a series of "gentle nocturnal ruminations" recorded in the dark for BBC Radio 4, which he created with Peter Curran. It was first broadcast during April 2014 with the fourth series broadcast in 2017.
His first play was Dealer's Choice, which he also directed. Set in a restaurant and based around a game of poker (and partly inspired by his own experiences with gambling addiction), it opened at the National Theatre in February 1995, and won the 1995 Evening Standard Award for Best Comedy.
After Miss Julie, a version of the Strindberg play Miss Julie, was broadcast on BBC television in the same year. In this, Marber moves the action to Britain in 1945, at the time of the Labour Party's victory in the general election, with Miss Julie as the daughter of a Labour peer. A stage version, directed by Michael Grandage, was first performed 2003 at the Donmar Warehouse, London by Kelly Reilly, Richard Coyle and Helen Baxendale. It later had a production at the American Airlines Theatre on Broadway in 2009.
His play Closer, a comedy of sex, dishonesty, and betrayal, opened at the National Theatre in 1997, again directed by Marber. This too won the Evening Standard award for Best Comedy, as well as the Critics' Circle Theatre Awards and Laurence Olivier awards for Best New Play. It has proved to be an international success, having been translated into thirty languages. A screen adaptation, written by Marber, was released in 2004, directed by Mike Nichols and starring Julia Roberts, Jude Law, Natalie Portman, and Clive Owen.
In Howard Katz, his next play, Marber presented very different subject matter: a middle-aged man struggling with life, death and religion. This was first performed in 2001, again at the National Theatre, but was less favourably received by the critics and has been less of a commercial success than some of his other work. A new production by the Roundabout Theatre Company opened Off-Broadway in March 2007, with Alfred Molina in the title role. A play for young people, The Musicians, about a school orchestra's visit to Russia, was performed for the National Theatre's Shell Connections programme in 2004, its first production being at the Sydney Opera House.
Don Juan in Soho, his contemporary rendering of Molière's comedy Don Juan, opened at the Donmar Warehouse in 2006, directed by Michael Grandage and with Rhys Ifans in the lead role.
He also co-wrote the screenplay for Asylum (2005), directed by David Mackenzie, and was sole screenwriter for the film Notes on a Scandal (2006), for which he was nominated for an Academy Award for Best Adapted Screenplay at the 79th Academy Awards.
In June 2015, his play, The Red Lion, opened at the National Theatre.
In 2016 he directed a revival of Tom Stoppard's play Travesties at the Menier Chocolate Factory in London which, after a sell-out run, transferred with the same cast to the Apollo Theatre in the West End. The revival was nominated for five Olivier Awards and in Spring 2018 will transfer to Broadway with Marber directing..
Marber's theatre directing credits include Blue Remembered Hills by Dennis Potter (National Theatre), The Old Neighbourhood by David Mamet, (Royal Court Theatre, London) and The Caretaker by Harold Pinter, (Comedy Theatre, London). In 2004, Marber was Cameron Mackintosh Professor of Contemporary Theatre at Oxford University.
Marber is a director of Lewes FC, driving forward a scheme for the club to be community owned since July 2010.
Since 2002, Marber has been married to actress Debra Gillett. They have three children.