The Predators gave Forsberg No. 9 on Saturday.
Forsberg was acquired in the trade that sent Martin Erat to Washington.
The 18-year-old Forsberg was Washington's top draft selection in 2012 at No. 11 overall. He received the 2013 Golden Cage Award in Sweden as the top junior player after getting 33 points in 38 games this season.
He also helped Sweden win the 2012 World Junior Championships and was captain of the silver medal winners at the 2013 World Juniors.