The Flames bought out the final season of the defenseman's three-year, $10.5 million contract ($3.5 million average annual value) on Aug. 2.
"I didn't see it playing out like this," Stone said Thursday when the Flames opened training camp. "I didn't know that this was even possible, but it was a good day yesterday. I'm happy to be back here. Good group of guys, great city, I live here in the summertime. So it was a good fit."
The 29-year-old had five assists in 14 games last season. He missed about four months after being diagnosed with blood clots in his arm Nov. 22.
General manager Brad Treliving said defenseman Juuso Valimaki tearing the ACL in his right knee in mid-August led to the Flames bringing back Stone.
"Even at the time we bought out Mike, we knew we needed some more depth on the blue line," Treliving said. "… [We] continued a dialogue with Mike (after Valimaki's injury), and it made sense for both sides."
Selected by the Phoenix Coyotes in the third round (No. 69) of the 2008 NHL Draft, Stone has 117 points (29 goals, 88 assists) in 439 games with the Coyotes and Flames.