General manager Ray Shero announced the moves Tuesday.
The 25-year-old Josefson got a one-year, $1.1 million contract and Gazdic signed a one-year, two-way contract worth $700,000.
Gazdic spent the last three seasons with the Edmonton Oilers. Last season, the 26-year-old only played in 29 games and had one goal.
So far in his six-year career with New Jersey, Josefson has 17 goals and 33 assists in 238 games. Last season, Josefson recorded career highs with 10 assists and 14 points.
Josefson joins defenseman Jon Merrill and forwards Beau Bennett and Devante Smith-Pelley as players who have recently re-signed with the Devils.
(TM and © Copyright 2016 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2016 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)