Elliott, 25, was acquired Friday from the Ottawa Senators in exchange for goalie Craig Anderson. He's a Canadian citizen and needed to have visa and immigration issues resolved in order to join the U.S.-based Avalanche.
With Elliott on board -- he'll wear jersey No. 30 -- goalie John Grahame has been returned to the Lake Erie Monsters in the American Hockey League. Grahame was Peter Budaj's backup for two games.
Elliott went 13-19-8 this season with three shutouts, a 3.19 goals-against average and .894 save percentage for the Senators. He posted a 29-18-4 record last year with five shutouts, a 2.57 average and a .909 save percentage.
"For some reason, things didn't click for guys," he said following the trade. "Nobody's having a breakout season in Ottawa. It's tough. I think that's why changes come. Guys are being sent different ways. I think it's good for everybody to get a different scenery. I'm no different. Hopefully that change will be beneficial."
The Avalanche's 4-3 win in St. Louis on Tuesday night ended the team's losing streak at 10 games.