Jonsson began playing for Leksands IF of Elitserien in 1999. Shortly after the season ended, he was drafted in the first round of the 2000 NHL Entry Draft by the Boston Bruins. Although the Bruins continually showed interest in him, attempting to sign him several times, they ran into issues with the NHL Collective Bargaining Agreement, which now states that European prospects will no longer remain indefinite property of the teams that draft them. As a result, the Bruins chose not to sign him and decided to instead receive the 37th overall pick in the 2006 Draft as compensation. The Bruins selected Yuri Alexandrov, a Russian defenseman who would play 66 games with the Providence Bruins during the 2010-11 AHL season before returning to Russia in 2011.