He rose to prominence with, winning three league titles and a cup, and scoring a goal to knock Milan out of the Union of European Football Associations Champions League. In 1998 he joined, but was troubled by injury during his five seasons there before retiring. In a two-year international career, Heggem earned 20 caps for Norway, scoring once in his debut match.
He was part of their squads at the 1998 Fédération internationale de football association World Cup and Union of European Football Associations Euro 2000.
Heggem made his professional debut with on 21 April 1995 against Kongsvinger in the Norwegian Premier League. He is best remembered by some for the goal in the away match against Milan in the 1996-1997 Union of European Football Associations Champions League when sensationally beat the Italian giants, thereby advancing to the Champions League quarter-finals.
After the 1998 Fédération internationale de football association World Cup, Heggem transferred to for £3.5 million. His first two seasons at Anfield were splendid, but he was unfortunately plagued by hamstring injuries.
After being injured in the 2000 European Championship he rarely appeared during the 2000-2001 treble-winning season, and during the next two seasons he did not appear in the lineup at all.
Heggem left when his contract ended in the summer of 2003, and shortly thereafter retired from football. Heggem made his national team debut on 25 February 1998 against France, scoring a goal in the 3–3 draw at the Stade Velodrome in Marseille. However, in the second match against First Revision Yugoslavia, he left the pitch injured after 35 minutes to be replaced by his teammate Stig Inge Bjørnebye, and Norway eventually were eliminated.
Heggem is currently the owner and manager of the salmon fishing business Aunan Lodge on the river Orkla in Sør-Trøndelag.
He is also an official patron of A.F.C., an independent football club owned and run by supporters. He is also a regular at home matches, and was also at the 2005 Union of European Football Associations Champions League Final in Istanbul.