The team announced the deal Friday.
The 17-year-old Forsberg, the 11th overall pick in last month's draft, will earn $832,500 if he plays in the NHL and $70,000 in the AHL.
Forsberg was Sweden's youngest player in the 2012 World Junior Championship. Team Sweden won its first gold medal since 1981 and Forsberg had one assist in six games.
In 43 games with Leksand of Sweden's Senior League last season, Forsberg had eight goals and nine assists.
Forsberg is training with the Capitals in their development camp, and the team says he's expected to play for Leksand again this season.