Terreri was drafted by the New Jersey Devils in the fifth round (85th overall) of the 1983 NHL Entry Draft. He attended Providence College from 1982 to 1986, and was the MVP of the 1985 Hockey East postseason tournament following a 2–1 double-overtime victory over top-seeded Boston College at the Providence Civic Center, and the MVP of the 1985 NCAA Men's Ice Hockey Championship, despite a 2–1 loss in the championship game to RPI at Joe Louis Arena.