Montoya played in 31 games with the New York Islanders during the 2011-12 season, going 9-11-5 with a 3.11 goals-against average and a save percentage of .893. He missed much of the second half of the season due to a concussion suffered when he was run over by Winnipeg forward Evander Kane in a game in mid-December.
The 27-year-old Chicago native was taken by the New York Rangers with the sixth pick in the 2004 NHL Draft. He has played in 57 career games with the Islanders and Phoenix Coyotes, posting a 21-17-10 career record, a 2.76 goals-against average and a save percentage of .906.
Montoya figures to back up Ondrej Pavelec, who signed a five-year, $19.5 million contract with the Jets last week.