Gunderson's contract is worth $1.95 million and Stone signed for $700,000, the club said.
Gudbranson, 29, has played 10 NHL seasons for six teams: Florida, Vancouver, Pittsburgh, Anaheim, Ottawa and Nashville. He has 77 points (21 goals, 56 assists) and 640 penalty minutes in 563 games.
The 31-year-old Stone is also a 10-year veteran. He has spent the past five seasons with the Flames and had four points in 21 appearances last season.