Dillane was born in London, to an Australian surgeon father and an English mother. He read history and political science at the University of Exeter and afterward became a journalist for the Croydon Advertiser. Unhappy in his career, he read how actor Trevor Eve gave up architecture for acting and was thus inspired to enter the Bristol Old Vic Theatre School.

Dillane is a distinguished theatre actor and his notable roles include Prior Walter in Angels in America (1993), Hamlet (1994), Clov in Samuel Beckett's Endgame (1996), Uncle Vanya (1998), Glen Foy in Goal, Henry in Tom Stoppard's The Real Thing for which he won a Tony (2000) and a one-man version of Macbeth (2005).

On screen, Dillane may be best known for his portrayal of Horatio in Franco Zefferelli's film adaptation of Hamlet, with Mel Gibson in the title role.

He played Michael Henderson in Welcome to Sarajevo (1997), a character based on British journalist Michael Nicholson. He is also known for his portrayal of Leonard Woolf in The Hours (2002) and of legendary English professional golfer Harry Vardon in The Greatest Game Ever Played (2005).