Stillman, who becomes an unrestricted free agent on July 1, had to waive his no-trade clause in order for the trade to proceed. He is earning $3.5 million this season in the final year of a three-year contract.
"This was a good opportunity for us to add some experience," Hurricanes general manager Jim Rutherford said in a release. "Cory adds more depth to our forward lines and we are familiar with what he is capable of doing offensively."
Stillman, who has won Stanley Cups with Carolina and Tampa Bay, suffered a fractured disk in his back in early December and missed 12 games. In 44 outings this season, the 37-year-old Peterborough, Ontario, native has seven goals and 16 assists with a plus-3 rating.
Drafted by the Calgary Flames in the first round (6th overall) in 1992, Stillman spent time with St. Louis, Tampa Bay, Carolina and Ottawa before being traded to the Panthers in 2008.
Stillman is earning $3.5 million this season in the final year of a three-year contract.
Carter signed with the Anaheim Ducks as a free agent in 2006 and saw his first NHL action the following season.
In 2009-10, the 27-year-old from White Bear Lake, Minnesota, was traded to Carolina for Stefan Chaput and Matt Kennedy. In 170 NHL games, Carter has 12 goals and 20 assist, a minus-3 rating and 163 penalty minutes.
Carter is in the final year of a three-year, $1,875,000 contract and will become an unrestricted free agent on July 1.