Under terms of the agreement announced Monday, Wilson receives $3.75 million in 2015-16 and $4 million each of the next three seasons. Wilson was a restricted free agent.
The 25-year-old Wilson set career highs in goals (20) and points (42) and tied a personal best in assists (22) in 2014-15. His plus-minus rating of plus-19 led the Predators.
Wilson scored five goals in six games during the Predators' first-round playoff loss to the eventual Stanley Cup champion Chicago Blackhawks.
Wilson, who is 6-foot-1 and 216 pounds, has 77 career goals and 101 assists in 368 NHL games. He has spent his entire NHL career with Nashville.