The deal carries an average annual value of about $2.85 million.
Sissons, who was scheduled for arbitration on July 26, becomes the 21st player this summer to settle a deal before their meeting date.
The 25-year-old tallied a career-high 15 goals and 30 points in 75 games for the Predators last season.
Nashville's 50th overall pick at the 2012 NHL Draft, Sissons has recorded 37 goals and 77 points in 265 career contests.
Long-term contracts with low average annual values are rare in the NHL, but this isn't the first time Predators general manager David Poile has signed a player to such a deal. In 2016, he inked forward Calle Jarnkrok to a six-year, $12-million pact.