The 32-year-old from Oshawa, Ont., has played a total of 10 professional seasons with Carolina and with the Toronto Maple Leafs.
Harrison has also played for the Toronto Marlies and with teams in Oshawa, Brampton, St. John's
Jets general manager Kevin Cheveldayoff told reporters that the team is working to have Harrison in place in time for Friday night's home game against the Boston Bruins.
The team made the move to shore up the blue-line following several key injuries. Toby Enstrom, Zach Bogosian, Jacob Trouba and Mark Stuart are all currently out of the lineup.
In addition to announcing the acquisition of Harrison, the Jets also announced that they've placed Trouba on the injury reserve list retroactive to Dec. 14.