Hagman, a center, was selected in the sixth round (No. 104) of the 1975 NHL Draft by the Boston Bruins. He played 237 NHL games for the Bruins and Edmonton Oilers, finishing with 145 points (56 goals, 89 assists), and had seven points (five goals, two assists) in 20 Stanley Cup Playoff games.
He also played more than 400 games in SM-Liiga, Finland's top pro league, and helped HIFK win the national championship in 1983. He played for Finland in four World Championships, three Canada Cup tournaments and the 1976 Innsbruck Olympics.
After his playing career ended, Hagman coached a number of teams in Finland. He was inducted into the Finnish Hockey Hall of Fame in 1995.
His son, Niklas Hagman, played in 770 NHL games from 2001-12 with the Florida Panthers, Dallas Stars, Toronto Maple Leafs, Calgary Flames and Anaheim Ducks.