The three-year deal is worth $3.575 million annually, according to a source.
Backlund scored 10 goals and 27 points in 52 regular-season games last season after missing 30 games because of injury.
In 11 playoff contests, the 26-year-old native of Sweden had one goal and one assist -- with his lone goal in overtime against the Anaheim Ducks in Game 3 of the first round.
Backlund, who was drafted by the Flames 24th overall in the 2007 NHL draft, set career highs in 2013-14 with 18 goals and 39 points in 76 games. He has played 298 career games with Calgary after making his NHL debut in 2009.
Information from The Associated Press was used in this report.