Stempniak will earn $5 million, while Sarich agreed to a deal worth $4 million on Friday.
Stempniak had 14 goals and 14 assists in 61 games for Calgary last season. He has 129 goals and 146 assists in 517 career games with St. Louis, Toronto, Phoenix and the Flames.
Sarich, a 13-year NHL veteran, has 20 goals and 126 assists in 887 career games while also spending time with Buffalo and Tampa Bay. He had one goal and six assists in 62 games with the Flames last season.
The Flames also signed center Blair Jones to a two-year deal worth $1.3 million. The 25-year-old had three goals and five assists in 43 games with Calgary and Tampa Bay last season.