General manager Ray Shero announced the moves on Tuesday.
The 25-year-old Josefson got a one-year, $1.1 million contract; Gazdic signed a one-year, two-way contract worth $700,000.
Gazdic spent the past 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 for the Devils, Josefson recorded career highs with 10 assists and 14 points.