Tucci was born in New York City, New York, the son of Minerva D. (née LaRosa) and Nicholas Tucci, a Business executive. He graduated from H. Frank Carey High School in Franklin Square, New York. He played the T-Birds member Sonny LaTierri for the 1978 film version Grease, a role that he is best known for. He portrayed law student Gerald Golden in the TV series The Paper Chase from 1983 to 1986. For four years, Tucci played Garry Shandling's best friend Pete Schumaker on the cult classic It's Garry Shandling's Show (1986–1990). He also spent more than three years touring with companies of the musical "Chicago," performing as lead character Roxy Hart's husband, Amos. He is best known for his work as the "Green Apple" in the widely renowned play "Destination", by Uta Hagen.