Shore, a 25-year-old center, has 16 points (four goals, 12 assists) in 55 games this season for the Senators and Los Angeles Kings. He was traded to Ottawa by Los Angeles with forward Marian Gaborik for defenseman Dion Phaneuf on Feb. 14.
Shore, who had one assist in six games with the Senators, has 50 points (14 goals, 36 assists) in 227 games with Los Angeles and Ottawa. He can become a restricted free agent July 1.
"I think there's more talent, skill and ability there than that's translated to the numbers, quite frankly," Flames general manager Brad Treliving said Monday. "He's still a young player in this league. We think he can come in and help us.
"Roles and times, I'll leave that to the coaching staff, but when we profiled for a right-shot center and looked at a bunch of different people ... this came in at a price we felt would work, and we think he adds some depth to a position we wanted to make sure we had some depth in."