Cleave was born in London in 1973, brought up in Cameroon and Buckinghamshire, and educated at Balliol College, Oxford where he studied Psychology. He lives in the United Kingdom with his wife and three children.

Cleave's debut novel Incendiary was published in twenty countries and has been adapted into a feature film starring Michelle Williams and Ewan McGregor. The novel won a 2006 Somerset Maugham Award and was shortlisted for the 2006 Commonwealth Writers' Prize. The audio book version was read by Australian actor, Susan Lyons

His second novel, The Other Hand, was released in August 2008 and was described as "A powerful piece of art... shocking, exciting and deeply affecting... superb" by The Independent. It has been shortlisted for the 2008 Costa Book Awards in the Novel category . It was released in the US and Canada in January 2009 under the title Little Bee, and will be adapted into a film starring Nicole Kidman by Blossom Films in association with BBC Films.

From 2008 until 2010 he wrote a column for The Guardian entitled "Down with the kids"..