The Wild announced the trade on Tuesday, one day before the NHL deadline for dealing.
The 33-year-old Russian has a 5-8-5 record in 20 games for the Oilers this season with a 3.01 goals-against average. His save percentage is .913. Bryzgalov has 38 games of playoff experience over five postseasons with Anaheim, Phoenix and Philadelphia.
The pick sent to Edmonton was originally acquired last year from Buffalo in the trade that brought Jason Pominville to Minnesota.
This team has been a real treat to say you've been the head coach of them. I'm extremely proud of this group ... after the disappointment of (the Game 6 loss) is digested, it's always a lot easier as a coach when your team has emptied its tank, and that team emptied its tank for me for three months.
— Senators coach Dave Cameron after getting eliminated in the first round by the Canadiens