Both signings were announced Wednesday.
Bass' contract will be worth $575,000 at the NHL level and $150,000 at the AHL level in 2016-17. His deal will be worth $650,000 at the NHL level and $150,000 at the AHL level in 2017-18.
The 29-year-old Bass split time between the Nashville Predators and their AHL affiliate in Milwaukee this season. He played 17 games for Nashville. He had four goals and five assists in 39 games with Milwaukee.
Bass has appeared in 66 career NHL games with Nashville, Ottawa and Columbus since 2007-08.
Gunnarsson, 24, has spent the past two seasons with the Malmo Redhawks of the Swedish Hockey League.