The Hurricanes will acquire a third-round selection in the 2016 draft. The team says the other pick will be in this year's draft, a fifth-round selection if the Jets make the playoffs and a sixth-rounder if they don't.
The 26-year-old Tlusty had tallied 76 goals and 69 assists in 322 games with Carolina over parts of six seasons. His career-highs of 23 goals and 38 points came during the lockout-shortened 2012-13 season.
Winnipeg hosts St. Louis on Thursday, while Carolina hosts Washington on Friday.