General manager David Poile announced the deal Friday.
Jarnkrok has 27 points in 86 career NHL games since his debut with the Predators on March 21, 2014, and he scored five points in his first five NHL games after Nashville acquired him in a trade from Detroit on March 5, 2014. That is the second-longest point streak by a Nashville player to start his NHL career.
Jarnkrok played in 74 games last season and all six playoff games. He also had an assist in each of his first two postseason games.
He was the 51st draft pick by Detroit in 2010. He also has played five international competitions for Sweden the past seven years.