Terms of the deal were not immediately disclosed.
Limited by injury in 2020-21, Bertuzzi appeared in only nine games. During those appearances, he managed to score five times and add two assists.
The 26-year-old enjoyed a career-year the season before, setting personal bests in assists (27), points (48) and penalty minutes (40).
Originally drafted by the Red Wings 58th overall in 2013, Bertuzzi has appeared in 208 games since making his NHL debut, picking up a total of 54 goals and 72 assists.