The 31-year-old left-winger had 69 points (22 goals, 47 assists) in 79 games in his return to Calgary last season.
The deal was confirmed Saturday by Flames general manager Jay Feaster.
Tanguay had 139 points (40-99) in 159 games for Calgary between 2006-'08. He was selected with the 12th overall pick by the Colorado Avalanche in the 1998 draft.
Calgary also made a trade Saturday, dealing veteran defenceman Robyn Regehr, right-winger Ales Kotalik and their second-round draft pick in 2012 to the Buffalo Sabres for defenceman Chris Butler and centre Paul Byron.