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.
I don't have a crystal ball. Predicting is a real complicated thing. If we stay healthy, have enough depth and get the good goaltending we think we're going to have, you can go all the way. But a lot of things have to happen. There's going to be a lot of teams that think the same thing. Everyone made deals. We're all are optimistic about where we'll end up.
— Rangers general manager Glen Sather after being asked if he's constructed a team that can win the Stanley Cup before their 4-1 win against the Predators on Monday