Berenger was born Thomas Michael Moore in Chicago, on May 31, 1949, to a Catholic family of Irish ancestry with his great-grandfather and grandmother settling in Chicago. He has a sister, Susan. His father was a printer for the Chicago Sun-Times and a traveling salesman.
Moore graduated in 1967 from Rich East High School in Park Forest, Illinois. He studied journalism at the University of Missouri in Columbia, Missouri, but decided to seek an acting career following his graduation in 1971 with a Bachelor of Arts degree. Moore selected "Berenger" as his professional name after he was forced to change his surname professionally, as there was already a "Tom Moore" in the Actors' Equity Association.