Greg Montesi started out internationally when he won a bronze medal in single sculls at the 1976 World Junior Championship. He competed at both the 1984 and 1988 Olympics in quadruple sculls, and at the 1986 World Championships in double sculls. Montesi rowed at the Salisbury School in Salisbury, Connecticut, where he was US Junior single sculls champion in 1977, and later rowed at Brown University, before transferring to the US Naval Academy, where he graduated in 1982. He was later inducted into the Naval Academy Hall of Fame. Montesi served in the US Marine Corps before settling in the suburban Boston area with his family.