The defenceman had one goal and adding six assists for seven points along with nine penalty minutes in 33 games the past season.
For his career, which began in Columbus, Russell has 23 goals and 72 assists for 95 points in 364 regular season games, with 145 penalty minutes.
The Blues receive a fifth round pick in the 2014 NHL Draft.
The Flames moved to address their goaltending issue, signing Finnish netminder Karri Ramo to a two-year deal.
Ramo was drafted in 2004 by Flames general manager Jay Feaster when he held that post in Tampa Bay.
The 27-year-old Ramo appeared in 48 games with the Lightning but then headed back overseas, spending the last three seasons in the KHL.
Longtime Calgary goalie Miikka Kiprusoff has yet to announce officially whether he will continue his NHL career. The Flames earlier this off-season signed 26-year-old goalie Reto Berra, who's played entirely in his native Switzerland.
In addition, the Flames announced that young forwards Corban Knight and Greg Nemisz have been signed.