Born in Kumla, Jonson started playing youth football with IFK Kumla and Karlslunds IF. He moved to Örebro SK in 1992, where he got his senior debut in the top-flight Allsvenskan championship. He moved to league rivals Helsingborgs IF in 1996, and made his Swedish national team debut in February 1996. He won the 1999 Allsvenskan championship with Helsingborg, before leaving the club at the end of the 1999 season. He moved abroad to join Danish club Brøndby IF in the Danish Superliga championship. He was brought in by Brøndby's new manager Åge Hareide, and Jonson played several games as a striker, before settling as a left-sided winger. He showed his goalscoring abilities for Brøndby on a number of occasions. In the 2001–02 UEFA Cup tournament, Brøndby had lost 1–3 away to Croatian club NK Varteks. In the return game, Jonson scored a hat-trick which guided Brøndby to a 5–0 victory and advancement in the tournament, on a 6–3 aggregate. Jonson also scored a hat-trick in an April 2002 Superliga game, when Brøndby won 5–0 against Akademisk Boldklub, and helped the club win the 2001–02 Superliga championship. He was a part of the Swedish national team squad at the 2002 World Cup, where he took part in two games as a substitute, before Sweden were eliminated. He was Brøndby's league topscorer with 11 goals in the 2002–03 Superliga season, and helped the club win the 2003 Danish Cup trophy. He was called up to the Swedish national squad for the 2004 European Championship. He started the tournament on the bench, but was brought on as a substitute and eventually secured himself a place in the starting line-up. He played in three of Sweden's four games, and scored a goal against Denmark, which secured Sweden advancement from the preliminary group stage. After the 2004 European Championship, Jonson looked to leave Brøndby. In August 2004, he moved to England and joined the newly promoted FA Premier League side Norwich City. He transferred from Brøndby for an undisclosed fee, which was believed to be around £850,000. He struggled to make an impact in the Premier League, and left Norwich after one season. In 2005, he returned to Sweden to play for Djurgårdens IF. In his first season with the club, he helped Djurgårdens IF win the Double of both the 2005 Allsvenskan and Svenska Cupen trophies. He represented Sweden at the 2006 World Cup, where he took part in all Sweden's four matches. He started the tournament as a substitute, but was included in Sweden's starting line-up for the final two games before elimination. He ended his national team career in August 2006. Jonson ended his career after the 2011 season, and played his last game on 23 October 2011.
