Andersson was selected in the 4th round (68th overall) of the 1989 NHL Entry Draft by the Quebec Nordiques, while he was playing in his native Sweden for Västra Frölunda HC.

At the age of 20, he left Frölunda to play in the American Hockey League (AHL) for the Nordiques' affiliate, the Halifax Citadels.

He finished that year with the Islanders, and played another two before signing with the San Jose Sharks prior to the 1997–98 season.

He never played in the NHL for the Leafs, and was instead sent to the IHL's Chicago Wolves until he traded back to the Islanders on 17 August 1999 for Craig Charron.

On 9 March 2011, Andersson decided to retire completely from hockey, having played 763 games for Frölunda HC.