The Togliatti, Russia native won the 2007 Stanley Cup with Anaheim and earned a Bronze Medal in the 2002 Winter Olympics with Team Russia.
Bryzgalov has played in 425 NHL games, with a win-loss record of 208-149-45. He has a career NHL goals against average of 2.55, a save percentage of .913, and 30 shutouts.
He was originally selected in the second-round, 44th overall, in 2000 by Anaheim.
Bryzgalov will be sent to the Oilers' AHL affiliate in Oklahoma City for conditioning before joining Edmonton.