Harmon was born in Burbank, California, the youngest of three children. His parents were Heisman Trophy–winning football player and broadcaster Tom Harmon and actress, model, and artist Elyse Knox (née Elsie Lillian Kornbrath). Harmon has two older sisters, the late actress and painter Kristin Nelson, who was divorced from the late singer Rick Nelson, and actress and model Kelly Harmon, formerly married to car magnate John DeLorean. His maternal grandparents were Austrian immigrants.

College football
After graduating from high school at Harvard-Westlake School, Harmon completed a two-year associate degree at Pierce College in Los Angeles. After his sophomore season at Pierce, Harmon received offers from major college football programs, ultimately choosing UCLA over Oklahoma. The Sooners finished second in the nation in 1971, while the Bruins were a preseason top-20 selection and stumbled to a 2–7–1 record, placing last in the Pac-8.

After transferring to the University of California, Los Angeles, he started at quarterback for the 1972 and 1973 Bruins.

During his first game, his UCLA team produced a stunning upset of the two-time defending national champion Nebraska Cornhuskers. The Bruins were an eighteen-point home underdog to the top-ranked Huskers but won 20–17 on a late field goal by Efren Herrera under the lights of L.A. Coliseum.

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