The 29-year-old native of Kiev, Ukraine, originally agreed to terms with Ufa on Tuesday.
Babchuk played in just seven games with the Flames this season, primarily due to suffering a shoulder injury, registering one assist and a minus-1 rating.
He played in 31 games with Donestsk of the KHL during the NHL lockout, tallying one goal and two assists.
In 289 career NHL regular-season games with the Chicago Blackhawks, Carolina Hurricanes and Flames, Babchuk has accumulated 36 goals and 71 assists for 107 points.
Babchuk was originally drafted 21st overall by the Blackhawks in the 2002 NHL Entry Draft.