Varma was born in Bath, Somerset, the only child of an Indian father and a Swiss mother who was of part Genoese Italian descent; her parents were relatively elderly and were often mistaken for her grandparents. She was a member of Musical Youth Theatre Company and graduated from the Royal Academy of Dramatic Art (RADA) in London, in 1995.
Varma has had a number of television and film roles, including Kama Sutra: A Tale of Love in 1997 and Bride and Prejudice in 2004, and the young Roman wife Niobe during the first season of BBC/HBO's historical drama series Rome. Her character appeared briefly in the second season of the award-winning series when it aired on 14 January 2007.
In 2006, she played Suzie Costello in the first and eighth episodes, "Everything Changes" and "They Keep Killing Suzie", of BBC Three's science-fiction drama series Torchwood. She appeared as Dr Adrienne Holland in the CBS medical drama 3 lbs which premiered on 14 November 2006 and was cancelled on 30 November 2006 due to poor ratings. Varma guest starred in the fourth-season premiere of hit US detective drama Bones as Scotland Yard Inspector Cate Pritchard. She also played the role of Zoe Luther in the first series of the BBC drama Luther.
Varma played the role of Ilsa Pucci in the second season of the Fox series Human Target until the show was cancelled on 10 May 2011.
Varma played the role of Ellaria Sand, the paramour of Oberyn Martell in season 4 of the HBO show Game of Thrones, and reprised the role in seasons 5, 6 and 7.
She lent her voice to the Circle mage Vivienne, in the 2014 role-playing video game Dragon Age: Inquisition.
In 2016, she played the lead role of DC Nina Suresh in the eight-episode British television drama Paranoid, streamed worldwide on Netflix.
In 1997, Varma played Bianca in Shakespeare's Othello at the National Theatre, London. In 2000 to 2001, she appeared in Harold Pinter and Di Trevis's NT stage adaptation of Pinter's The Proust Screenplay, Remembrance of Things Past, based on À la recherche du temps perdu, by Marcel Proust. In the summer of 2001, she played Gila in One for the Road, by Harold Pinter, at the Lincoln Center for the Performing Arts in New York City.
In 2002, she played Sasha Lebedieff in Ivanov by Anton Chekhov at the National Theatre and Bunty Mainwaring in The Vortex by Noël Coward at the Donmar Theatre, London. In 2004, she played Sabina in The Skin of Our Teeth by Thornton Wilder at the Young Vic Theatre Theatre, London. In 2008, she played Nadia Baliye in The Vertical Hour by David Hare at the Royal Court Theatre London. In 2009, she played Olivia in Shakespeare's Twelfth Night with Donmar West End at Wyndham's Theatre, London. In 2012, she played Jessica in Terry Johnson's Hysteria at the Theatre Royal, Bath. In 2013 she played Miss Cutts in The Hothouse by Harold Pinter in the Trafalgar Transformed season at Trafalgar Studios.
In 2014, Varma played Tamora, Queen of the Goths, in Lucy Bailey's "gore-fest" production of Titus Andronicus at Shakespeare's Globe. In 2015, she appeared alongside Ralph Fiennes in George Bernard Shaw's Man and Superman at the National Theatre.
Varma and her husband, fellow actor Colin Tierney, live with their daughter Evelyn in Hornsey, North London.