Gleason was born on May 4, 1939, in Jersey City, New Jersey, the son of Eleanor (née Doyle), a registered nurse, and George L. Gleason, a restaurateur, professional boxer, iron worker, and roofing manufacturer. Gleason was raised in Miami Beach, Florida. At age 16, he ran away from home and hitchhiked across the east coast, sleeping on beaches and playing baseball. He attended North Miami High School and Florida State University, where he played football. He signed a professional baseball contract with the Cleveland Indians, but played just briefly in two minor league seasons between 1959 and 1960.During that last season, a West Coast trip led to an introduction to sitcom icon Ozzie Nelson, which, in turn, led to an appearance on Ozzie and Harriet (as per Nelson's habit of hiring athletes for guest spots on the show). Suddenly, acting was an option, and an increasingly attractive one, given Gleason's stillborn baseball career. He moved to New York City, eventually joining The Actors Studio, where he would study for four years before moving to Los Angeles.