The 24-year-old Bourque has 30 goals and 44 assists in 220 career NHL games, all with Nashville. Bourque had three goals and 10 assists in 69 games this past season after collecting nine goals and 17 assists in 2013-14.
The Predators also announced the signings of forward Max Reinhart and free-agent defenseman Conor Allen to one-year, two-way contracts worth $575,000 when they're in the NHL and $80,000 when they're in the American Hockey League.
Allen has spent most of the past two-plus seasons in the New York Rangers organization. The Predators acquired Reinhart from the Calgary Flames on Wednesday for a conditional fourth-round draft pick.