The Wild also sent the rights to their second-round pick in the 2011 draft.
The 27-year-old Kobasew had one assist in seven games with the Bruins this season. He had 21 goals and 21 assists in 68 games last season, reaching the 20-goal mark for the third time in his career.
In other Bruins news, the team put hard-hitting winger Milan Lucic on long-term injured reserve with a finger injury, meaning he'll be out at least 10 games and 24 calendar days.
Lucic, who signed a three-year extension with the Bruins earlier this month, suffered the injury Friday night in a 3-0 win at Dallas. A team spokesperson said Sunday there would be no update on Lucic's status until general manager Peter Chiarelli addresses the media Monday afternoon.
ESPNBoston.com's Matt Kalman contributed to this report.