Sources told ESPN.com that the Oilers retained 24 percent of Scrivens' salary and cap hit.
Kassian had recently completed time in the NHL-NHLPA's Substance Abuse and Behavorial Health Program, and his future in Montreal seemed in doubt.
The Oilers hope Kassian, 24, will respond in what may be his last chance to make it in the NHL. For now, he will report to Edmonton's AHL farm team.
Scrivens was expected to be the backup goaltender for the struggling Canadiens in Tampa on Monday night. The Habs have lost nine of their 11 games so far in December, the prolonged injury absence of superstar goalie Carey Price being fully felt.
Scrivens went unclaimed on waivers before the season after being beat out for the No. 2 job in Edmonton by Anders Nilsson. He went 2-6-1 with Edmonton's AHL affiliate in Bakersfield with a 3.47 goals-against average and .893 save percentage.