A graduate of Saint Ignatius High School in Cleveland, Hegan began his major league career with the New York Yankees in 1964, also playing for the Seattle Pilots (for whom he hit the first home run in franchise history in his first at-bat with the team in 1969), Milwaukee Brewers, and Oakland Athletics as an outfielder and first baseman. He was one of two Pilots to represent the team at the All-Star Game in their lone year of existence, along with Don Mincher. He was a member of the 1972 World Champion Oakland Athletics, chiefly as a pinch hitter and defensive replacement for starting first baseman Mike Epstein. Hegan was the last batter in the (pre-renovation) Yankee Stadium, flying out to center field as the Yankees lost to Detroit, 8-5 on September 30, 1973. On September 3, 1976, he hit for the cycle. Hegan also held the American League record for most consecutive error-less games as a first baseman (178), until it was broken by Kevin Youkilis on September 7, 2007.
After his retirement from baseball as a player, Hegan spent the next twelve seasons as a television color commentator for the Brewers. In 1989 he was hired by the Cleveland Indians, and served as a commentator for the team on both radio and television. Beginning in the 2007 season, he worked exclusively on Indians radio broadcasts, paired with Tom Hamilton and later with Hamilton and Jim Rosenhaus in 2010 as part of a three-man broadcast team. In 2012, Hegan left the broadcast booth for a role with the Indians as an alumni ambassador. However, on May 23 of that year he filled in for former partner Hamilton, teaming with Rosenhaus to call a game against the Detroit Tigers.