Born in Bjärred, Andersson began his career with the local club, Bjärreds IF. In 1988, he moved on to Malmö FF, a team playing in the top national league.
In December 1992, Andersson went professional as he moved to Blackburn Rovers for a fee of £800,000, where he stayed for one year, making just 12 Premier League appearances. However, he is notable for being one of the first foreign signings by Blackburn Rovers, and one of the relatively small group of foreigners who appeared in the first season of the new Premier League in England. He scored once for Blackburn, in a 2–1 defeat to Sheffield Wednesday in the second leg of the 1992–93 Football League Cup semi-final.
His next step was to go to Germany in October 1993 and play for Borussia Mönchengladbach. There he won the DFB-Pokal with the team in 1995, but left the team as its performance deteriorated, in 1999.
In June 1999, Andersson signed for Bayern Munich for approximately DM 6 million. He made his debut on 22 August 1999 in a 2–0 away defeat to Bayer Leverkusen. His time with Bayern resulted in two Bundesliga championships as well as a DFB-Pokal and victory in the 2000–01 UEFA Champions League, despite missing his penalty in the final shootout.
Andersson moved to La Liga giants FC Barcelona in 2001 and spent three injury-plagued seasons there. Therefore he played only 19 league matches for the Blaugrana.
Malmö FF
For the 2004 season, Andersson came back to Malmö FF to play in the Swedish league again after 10 years. This year he captained Malmö FF who won their first Swedish league title in 15 years. He has twice been awarded Guldbollen as the Swedish footballer of the year, in 1995 and 2001. After suffering yet another knee injury during a Champions League qualifier against Swiss team FC Thun on 10 August 2005, Andersson announced his retirement from professional football on 12 August 2005. He was appointed as Manchester United's scout in Scandinavia in August 2010.
International career
Andersson earned a total of 96 caps for the Swedish national team, scoring three goals. He won a bronze medal in the 1994 FIFA World Cup. Andersson also played in the team that reached the semi-finals at UEFA Euro 1992. He was also part of the Swedish national squad that took part in Euro 2000, the 2002 FIFA World Cup and was a member of the Swedish squad that competed at the 1992 Summer Olympics in Barcelona. At Euro 2000, he received a red card for a hard foul on Belgium's Bart Goor. At the 2002 World Cup, in Sweden's last training session before their opening match against England, Andersson was injured and was not able to play in the tournament. He was replaced by Andreas Jakobsson.