The 26-year-old could have become an unrestricted free agent July 1. The contract has an average annual value of $3.5 million.
Stone had six points (two goals, four assists) in 19 games with the Flames after he was acquired Feb. 20 in a trade with the Arizona Coyotes. He scored one goal when the Flames were swept by the Anaheim Ducks in the Western Conference First Round.
A third-round pick (No. 69) by the Coyotes in the 2008 NHL Draft, he played 45 games for Arizona this season. He has 96 points (24 goals, 72 assists) in 324 NHL games.