In the trade announced Wednesday during the Maple Leafs' Winter Classic game against Detroit, the Hurricanes also received the rights to defenceman Dennis Robertson.
The 30-year-old Gleason was the Hurricanes' most physical forward and one of the longest-tenured players on the team. Only captain Eric Staal and 2006 Conn Smythe Trophy-winning goalie Cam Ward have been with the franchise longer.
The 33-year-old Liles has 15 hits and averaged 17 minutes of ice time in six games this season with the Maple Leafs. He was scratched from the Winter Classic.
Carolina general manager Jim Rutherford says Liles is a puck-mover who "can make a difference offensively" from the blue line.