Koteas was born in Montreal, Quebec, Canada, to a father who worked as a mechanic for the Canadian National Railways, and a milliner mother. His parents are both of Greek descent, from the Mani Peninsula and he is fluent in Greek speaker. Koteas attended Vanier College in Montreal before leaving to attend the American Academy of Dramatic Arts in New York City in 1981, of which he is a 1983 graduate. He was a member of the Academy's 1983–84 Production Company. He also attended the Actors Studio in New York City, where he studied acting under Ellen Burstyn and Peter Masterson.