Gustavsson has agreed to a three-year deal with Swedish club Linkoping, TVA Sports reports.
The Oilers assigned Gustavsson to AHL Bakersfield on Wednesday.
Gustavsson will be on the bench for Tuesday's meeting with San Jose, Jason Gregor of TSN 1260 reports.
Gustavsson cleared waivers Tuesday.
Gustavsson was put on waivers Monday.
Gustavsson gave up four goals on 17 shots in Sunday's loss to the Senators.
Gustavsson will start in goal Sunday against the Senators.
Gustavsson was battered for six goals on 31 shots in Thursday's loss to Philadelphia.
Gustavsson will start between the pipes in Thursday's road game against the Flyers.
Gustavsson made 31 saves on 33 shots in Sunday's overtime loss to the Wild.