Defenseman Taylor Ellington and a pair of fourth-round picks in the 2012 NHL entry draft were sent to the Blue Jackets in exchange for the 34-year-old Swede.
Pahlsson, a defensive specialist, has two goals and nine assists for 11 points in 61 games this season while racking up 66 goals and 127 assists for 193 points over 11 NHL seasons with Boston, Anaheim, Chicago and Columbus.
Meanwhile, the Canucks sent center Cody Hodgson to the Buffalo Sabres for right wing Zack Kassian.
A former first-round draft pick, Hodgson has picked up 16 goals and 17 assists in 63 games this season, while Kassian has collected three goals and seven points in 27 games for Buffalo.
Also as part of the trade, the Sabres sent defenseman Marc-Andre Gragnani to the Canucks for fellow blueliner Alexander Sulzer.
In a third deal, the Canucks obtained right wing Andrew Gordon from the Anaheim Ducks for defenseman Sebastien Erixon.