General manager David Poile announced the deal Monday.
Tolvanen, 22, just finished his first full NHL season. He scored 22 points in 40 games, and his 11 goals ranked fourth on the Predators as the most by a Nashville rookie since Filip Forsberg had 26 in 2014-15.
The 5-foot-10, 191-pound forward also had six power-play goals, tied for the second most among Nashville rookies all-time. His six-game point streak between March 21 and 30 tied for the second longest among those rookies.
The native of Vihti, Finland, tied for first among NHL rookies with four game-winning goals. He tied for second in power-play goals and was third with 12 power-play points. He had three multipoint games.
Tolvanen was the 30th overall draft pick in 2017 and has played in 47 career NHL games. He became the fifth-youngest player to debut at the age of 18 years, 343 days on March 31, 2018, against Buffalo. He played for Jokerit in the KHL and played for Finland in the 2018 Winter Olympics, where he had nine points in five games.
The Predators view Tolvanen as an important piece up front as they get younger overall. Nashville struggled out of the gate last season but rallied to make the postseason, where it lost to the Carolina Hurricanes in the first round.
The Associated Press contributed to this report.