Nashville sent forward Ryan Hartman and a conditional fourth-round pick in the 2020 NHL Draft in exchange for Simmonds.
Simmonds is in the final season of a six-year contract he signed Aug. 16, 2012. He can become an unrestricted free agent July 1. The 11-year NHL veteran has 27 points (16 goals, 11 assists) in 62 games this season with the Flyers.
The Los Angeles Kings originally selected Simmonds in the second round of the 2007 NHL Draft. The Flyers traded for him June 23, 2011, and he has scored at least 24 goals in six seasons with Philadelphia.
Simmonds has 471 points (242 goals, 229 assists) in 824 career regular-season games. He has 21 points (eight goals, 13 assists) in 42 playoff games.
Hartman can also become an unrestricted free agent July 1. He has notched 20 points (10 goals, 10 assists) in 64 games this season.
The Predators originally obtained Hartman in a trade with the Chicago Blackhawks on Feb. 26, 2018. He has 83 points (40 goals, 43 assists) in 226 career NHL games.
Nashville also traded for Minnesota Wild forward Mikael Granlund on Monday.