The deal was announced on Tuesday.
Zucker will have a two-way contract for this season and a one-way contract for next season. Players on one-way deals are paid the same, whether they are in the NHL or the AHL.
Zucker was one of the Wild's top prospects, but the 22-year-old fell behind last season due to inconsistency, injury and increased competition. Zucker had four goals and one assist in 21 games for the Wild and eight goals and five assists in 22 games for their AHL affiliate Iowa. Zucker had surgery in March to repair a tendon in his left quadriceps.
Zucker was the Wild's second-round draft pick in 2010.