Scott was born in Dublin in 1976, the son of Nora and Jim Scott. His mother was an art teacher, while his father worked at an employment agency. He is the second of three children; he has an older sister, Sarah, and a younger sister, Hannah. Scott was raised as a Catholic, but no longer practises.
He attended Gonzaga College while taking weekend classes at Ann Kavanagh's Young People's Theatre in Rathfarnham, and appeared in two ads on Irish television. At 17, Scott was chosen for a starring role in his first film Korea. He won a bursary to art school, but elected to study drama at Trinity College Dublin, leaving after six months to join Dublin's Abbey Theatre and then moving to London when he was 22. He once stated to the London Evening Standard that he always had a "healthy obsession" with acting.