Hornqvist, 23, is Nashville's first draft pick to score 30 goals, and he led the team with his 30 goals last season. That also marked the fourth-highest total in franchise history.
Hornqvist, from Sollentuna, Sweden, tied the franchise record and tied for second in the NHL with eight game-winning goals. He led the Predators, who announced the deal on Tuesday, with 10 power-play goals and finished tied for the team lead with 51 points off a franchise-record 275 shots in the season.
A seventh-round draft pick in 2005, the 5-foot-11, 186-pound forward led Nashville skaters with a plus-18 rating.