The Flames and Sarich agreed to an US$18-million, five-year deal within just a couple hours of the market opening.
Flames captain Jarome Iginla, defenceman Robyn Regehr and goaltender Mikka Kiprusoff are scheduled to become unrestricted free agents next July 1.
General manager Darryl Sutter was trying to hammer out extensions for both Iginla and Regehr.
"I think we're still working on the details of both of them," Sutter said Sunday. "There's a lot more to it than just money. We'll get it worked out."
Iginla, the NHL's scoring champion in 2002, is scheduled to make a salary of $7 million in the final year of his contract, while the pay for Regehr, one of the league's premiere shutdown defencemen, will be $2.052 million.
Kiprusoff would command a major raise on his $3.6-million salary as a free agent. He's spending his off-season at home in Finland.
Sutter isn't interested in long-distance negotiations and says he'll wait until the former Vezina Trophy winner is back in Canada before starting talks.
"You can make a lot of headway when everybody is the same room," he said.
Finding a top-four defenceman Sunday was the most pressing need for Sutter because Roman Hamrlik and Brad Stuart, who became free agents Sunday, looked to be too expensive to re-sign.
Sutter was in the market for a right-handed defenceman in the upper-20 age bracket capable of partnering with either Regehr or Dion Phaneuf.
The Flames had acquired 33-year-old Adrian Aucoin, another right-hander, from Chicago prior to the NHL draft June 22. Sutter wanted to get younger with his next transaction for the blue-line.
Sarich, 28, spent his last seven seasons with the Tampa Bay Lightning and helped the Lightning beat Calgary in the Stanley Cup final in 2004.
He said the last contact he'd had with Sutter before Sunday was shaking his hand on the ice after Game 7.
The six-foot-three, 210-pounder from Saskatoon had 15 assists in 82 games and was minus-six averaging 18 minutes a game last season.
Sarich is a durable player as he's played all 82 regular-season games four years running. He appeared in all 23 playoff games during the Lightning's Stanley Cup run.
"Areas where we have to improve, number one, was penalty killing and playing in our own zone and that's where Cory is a very good player, a shot blocker and really similar to Robyn to be quite honest," Sutter said.
"We've tried to make a point . . . of making sure we had one of the best defences in the game and we obviously felt with bringing Cory in, it makes us younger and better again."
Sarich has made his off-season home in Calgary since 2004, which accelerated signing a contract Sunday.
"I don't think this would have happened had I not lived in Calgary," he said. "I think this club is headed in the right direction. I've had the opportunity to play them in the playoffs a couple years ago and watching them in the playoffs, what they've done, there's no where but up to go with this team."
There were rumours prior to the draft that the Flames might deal forward Alex Tanguay, but Sutter shut down that speculation Sunday.
"We're not interested in anything . . . other than Alex being on our team. I'm making that very clear," he said.
Sarich, whose salary was $1.9 million last season, said Tampa Bay did not try to re-sign him and he couldn't resist the raise and the long-term deal Calgary dangled in front of him.
"It will take me into my early 30s and it's just a good fit for me," he said. "I'm just a guy that likes to stay put."