Janssen, 30, could have become an unrestricted free agent July 1.
In 24 NHL games this season Janssen scored a career-best three goals. In 27 games with the Devils' American Hockey League affiliate, the Albany Devils, he had three assists.
A 2002 fourth-round pick (No. 117) of the Devils, Janssen has six goals, 14 points and 774 penalty minutes in 336 NHL games with New Jersey and the St. Louis Blues.
Kozun, 24, was acquired by the Maple Leafs on Jan. 22, 2014 from the Los Angeles Kings in a trade for Andrew Crezcenzi.
Kozun had 17 goals and 29 assists in 75 American Hockey League games split between the Manchester Monarchs and Toronto Marlies this season.
The Los Angeles native had four goals and two assists in 14 playoff games for the Marlies. He has 196 points in 296 AHL games.
Kozun was selected by Los Angeles in the sixth round (No. 179) in the 2009 NHL Draft.