Bouton was born in Newark, New Jersey, the son of Gertrude (Vischer) and George Hempstead Bouton, an executive. He grew up as a fan of the New York Giants in Rochelle Park, New Jersey, where he lived until the age of 13. He lived with his family in Ridgewood, New Jersey until he was 15, when his family relocated to Homewood, Illinois. Bouton enrolled at Bloom High School, where he played for the school's baseball team. Bouton was nicknamed "Warm-Up Bouton" because he never got to play in a game, serving much of his time as a benchwarmer. Bloom's star pitcher at that time was Jerry Colangelo, who later would become owner of the Arizona Diamondbacks and Phoenix Suns. In summer leagues, Bouton did not throw particularly hard, but he got batters out by mixing conventional pitches with the knuckleball that he had experimented with since childhood.