Predators general manager David Poile announced the deal Monday.
Under terms of the contract, Sissons will make $575,000 at the NHL level and $100,000 at the AHL level in 2016-17. He will receive $650,000 each in 2017-18 and 2018-19.
Sissons, 22, has a goal and an assist in 19 games with the Predators this season. He also has been serving as the youngest captain in the history of the AHL's Milwaukee Admirals. Sissons has six goals and 10 assists in 33 games with Milwaukee.
Sissons was a second-round pick and the 50th overall selection in the 2012 entry draft.