Meagher played almost 700 games in the National Hockey League (NHL) with the Montreal Canadiens, Hartford Whalers, New Jersey Devils and St. Louis Blues.
Not drafted by a National Hockey League (NHL) team, Meagher's playing career began with the Boston University Terriers.
He played four seasons at Boston University, winning numerous awards, including being named to both the First and Second All-Star teams twice.
The 1981–82 season had Meagher playing full-time in the NHL, recording 24 goals while centering a line with Don Nachbaur and Warren Miller.
In 1989–90, a season in which he was also named team captain of the Blues, Meagher received the Frank J. Selke Trophy as the league's top defensive forward.