Backlund had four goals and seven assists in 41 games for Calgary last season. He has 15 goals and 31 assists in 138 career games with the Flames.
The native of Vasteras, Sweden, was the Flames' first round pick (24th overall) in the 2007 NHL draft.
"Mikael has an opportunity to step up and attempt to secure a top two-line centre position with our club," Flames general manager Jay Feaster said in a statement. "He is a very talented player who skates well, has excellent vision and possesses a strong skill set."