Andrews was born in Lambeth, London to Nirmala, a psychologist, and Stanley Andrews, a businessman, both Malayali Nasrani immigrants from Kerala, India. He was brought up in Wandsworth in the Methodist denomination of Christianity. Andrews described his upbringing as “very repressive”. At 16, while at Emanuel School, he fell in love with his 30-year-old mathematics teacher, Geraldine Feakins, whom he moved in with to escape his abusive home; their son, Jaisal, was born seven years later, in 1992. Andrews was shunned by his parents after this and they died before a reconciliation. He has said that he has forgiven them.

Andrews’s relationship with Feakins lasted from 1985 to 1991. Their son, Jaisal Andrews, was born in 1992. He was later in a relationship with actress Barbara Hershey in Los Angeles, starting in 1998. The couple separated briefly in 2005 and, during that time, Andrews had a son with Czech-French actress Elena Eustache. He and Hershey later reconciled, but in 2010, they announced that they had separated. Andrews was in an long custody dispute with Eustache over their son, and on 7 January 2009, he was granted sole legal and physical custody.

Andrews auditioned for drama school and was accepted at London’s Guildhall School of Music and Drama with Ewan McGregor and David Thewlis. His studies paid off when he won a role in Hanif Kureshi’s film London Kills Me (1991). Andrews starred in the 1993 BBC miniseries Buddha of Suburbia. He portrayed Kip Singh in The English Patient (1996) and Sayid Jarrah in the popular television series Lost (2004). In 2006, he was voted one of People magazine’s World’s Most Beautiful People. He starred in Kama Sutra: A Tale of Love (1996), Mighty Joe Young (1998), Bride and Prejudice (2004), and as Jafar in the American fantasy drama Once Upon a Time in Wonderland (aired 2013-14). In 2014, he provided the voice of Sabal in the video game Far Cry 4. From 2015 to 2017, he starred in the series Sense8 (created by The Wachowskis and J. Michael Straczynski) as Jonas. From 2018 to 2019, he co-starred as ex-MI6 and CIA officer Julian Cousins in the series Instinct, starring Alan Cumming and Bojana Novakovic.

He plays guitar and sings, while tap-dancing to his own tune as a hobby. He became a naturalised U.S. citizen on 27 May 2010.