Harris left Britain in the early 80s to attend Duke University in North Carolina. He auditioned for a college production and landed a role merely because he had an authentic British accent. (The director thought that would be a good influence on the American cast.) Harris was bitten by the acting bug and returned to Britain after graduation where he joined the Royal Shakespeare Company. Eventually returning to America, the tall redhead was cast as Hotspur in a 1990 off-Broadway production of "Henry IV".
Harris' first screen appearance was in "The Rachel Papers" (1989) which also marked the directorial debut of his older brother Damian. He played Tom Cruise's boozing, n'er-do-well brother in Ron Howard's "Far and Away" and had a small role as a British lieutenant in Michael Mann's "The Last of the Mohicans" (both 1992). Two years later, he won notice as one of the twin children of Dracula, with whom Suzy Amis falls in love in Michael Almereyda's "Nadja" and went on to portray an intellectually-challenged street cleaner in Wayne Wang and Paul Auster's "Smoke" and "Blue in the Face" (both 1995). Harris went on to play a truculent fur trapper in Jim Jarmusch's "Dead Man" (1995). Two films featuring Harris were premiered at the 1997 Sundance Film Festival, "Sunday" and "Hurricane". The actor also completed Michael Radford's "B. Monkey", opposite Asia Argento, Ivan Reitman's comedy "Father's Day", alongside Billy Crystal and Robin Williams and the Noel Pearson-produced "Gold in the Streets", with Ian Hart.