Rhys was born in Neath, Glamorgan, and studied at RADA, leaving with the Bancroft Gold Medal in 1985. After graduating, he obtained his first major screen role, in Absolute Beginners (1986). Since then he has seldom been off the stage and screen. His first US exposure was when American film Director Robert Altman cast Rhys, who was then still a student, as Theo van Gogh in Vincent and Theo opposite Tim Roth as Vincent.