Sullivan, 36, is a 15-year veteran who had 10 goals and 22 points for Nashville last season. He spent six seasons with the Predators, and has 682 career points. He signed a one-year contract, worth $1.5 million.
Kennedy, 24, had 21 goals and 45 points in 80 games last season with Pittsburgh. In 266 career NHL games, Kennedy, 5-foot-11 and 183 pounds, has 59 goals and 124 points. He signed a two-year contract worth $4 million.
Kennedy, a native of Sault Ste. Marie, Ontario, helped lead the Penguins to the 2009 Stanley Cup, with five goals and nine points that postseason.
The announcements came soon after Pittsburgh formally withdrew their one-year contract offer to free-agent forward Jaromir Jagr. A 1990 first-round draft pick of the Penguins, Jagr signed a one-year deal, worth $3.3 million, in Philadelphia.
Sullivan had two goals and three points as the Predators advanced to the second round of the Western Conference playoffs for the first time this season. A native of Timmins, Ontario, Sullivan has appeared in 890 games with the Devils, Maple Leafs, Blackhawks and Predators. He has 266 career goals.
Sullivan missed the entire 2007-08 season with a back injury, before returning on Jan. 10, 2009. Sullivan finished that season with 11 goals and 32 points in 41 games, winning the Bill Masterton Memorial Trophy for his perseverance, sportsmanship and dedication to the game.