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According to multiple reports, the contract is worth $68million, carrying an average annual value of $8.5million.
Last season Forsberg registered career-high figures, with 42 goals and 42 assists while playing in 69 games.
Forsberg just completed a six-year, $36million contract, and the 27-year-old would have become a free agent if a deal had not been signed by July 13.
The franchise's all-time leading scorer with 220 goals, Forsberg has only played at the NHL level for Nashville and has become an alternate captain.
He has 29 career goals and 53 career points in Stanley Cup playoff games, both franchise bests.
Forsberg was drafted 11th overall by the Washington Capitals in 2012 but was traded before making his NHL debut to the Predators for Martin Erat and Michael Latta.
The Predators were swept in the first round of the Stanley Cup playoffs last season by the eventual champions, the Colorado Avalanche. Nashville have made the postseason in four of the last five seasons but have failed to advance to the second round since 2018.