Varma is the only child of a South Asian Indian father and a Swiss mother who was part Genoese Italian. She was a member of Musical Youth Theatre Company. She graduated from the Royal Academy of Dramatic Art (RADA) in London in 1995.
In Game of Thrones, Varma plays the role of Ellaria Sand, the paramour of Prince Oberyn Martell. She joined the cast as a guest star in the fourth season, and was promoted to starring cast member in the fifth season.