The deal is worth $2.3 million a season, a source told ESPN.com's Pierre LeBrun.
Scrivens was acquired in a trade with the Los Angeles Kings on Jan. 15. The Spruce Grove, Alta., native is 3-4-0 with one shutout with the Oilers.
Scrivens said Monday: "It's great to be here in Edmonton playing at home."
The 27-year-old Scrivens made an immediate impression on his new team when he had 59 stops in a 3-0 win over San Jose on Jan. 29, setting an NHL regular-season record for saves in a shutout.
He is 10-9-4 for the season, including four shutouts and a league-leading .934 save percentage.
Information from The Associated Press was used in this report.