The deal is worth an average annual value of $675,000 in the NHL.
Shaw, 26, has played seven games for the San Diego Gulls of the AHL this season and has five points (two goals and three assists).
The Glace Bay, N.S., native has played for three different NHL teams, including 72 games between Anaheim and Montreal in 2017-18 when he had four goals and 10 assists.
Shaw has played 180 career NHL games for the Canadiens, Ducks, and Panthers and has 12 goals and 19 assists. He also played in 12 playoff games.
Shaw was originally drafted by Florida in the third round (76th overall) in the 2011 NHL draft.
The Jets also announced Sunday that they recalled defenceman Sami Niku from the AHL’s Manitoba Moose.