After starting his career with local club Vessigebro BK he moved to Halmstads BK in 1988. He played for the team until 1995, when he joined IFK Göteborg, with whom he won the Swedish Championships and played in the UEFA Champions League. After one year in Gothenburg, he moved on to England, where he was signed for £750,000 by Ron Atkinson for Sheffield Wednesday. He played for three seasons in Sheffield, where he became a fan's favorite and won the Player of The Season award the year the team was relegated. After relegation he was signed by Everton for £2.5 million where he played for from 2000 to 2003, until he moved back to Gothenburg, where he played from 2004 to 2008. After an initial retirement in 2008 Alexandersson worked at IFK Göteborg's youth academy, Änglagårdskolan. On 27 September 2009, newspapers reported that he was to make a comeback and would start training again on 29 September 2009. On 2 October 2009 it was revealed that Alexandersson has sign a contract for the rest of the season. After the season, he retired for good.
International career
He made his debut for the national team in 1993, and participated in 109 international games, scoring seven goals. His participation in the national team includes the 2002 FIFA World Cup, 2006 FIFA World Cup, Euro 2000 and Euro 2008. He was also a member of the Swedish squad that competed at the 1992 Summer Olympics in Barcelona. One of his goals came in Sweden's 1–1 draw against England, which he shot powerfully from outside the box and passed through David Seaman during the group stages of the 2002 World Cup. The day after Sweden's exit from Euro 2008 he decided that he would retire from the national team alongside Marcus Allbäck, however he also said that if it was needed, due to injuries, he would play for the national team again.
Personal life
Alexandersson was born in Halmstad on 29 December 1971 to father Lennart Alexandersson, a former Halmstads BK player. He grew up in Falkenberg, where he started playing football in the local club Vessigebro BK. In 1978, his brother Daniel Alexandersson, who was also a professional football player, was born. In 1988, he moved to Halmstad to play for Halmstads BK. He attended Falkenbergsgymnasieskola 1987-1990. Alexandersson married his wife Frida. The couple had first child Tilda in 1999 and son named Noah in 2001. While playing football, Alexandersson's family has lived in numerous places including Sheffield, Liverpool, and London before returning to Gothenborg.