The deal was completed Saturday at the NHL draft.
Regehr, a 12-year veteran who has spent his entire NHL career with the Flames, waived his no-trade rights in order for the deal to be completed.
Regehr has been mulling the trade for two days and took calls from Sabres general manager Darcy Regier and Sabres owner Terry Pegula.
"It's not just veteran leadership, it is size and experience. We added size as well. With the history he has and the age he is at, he has years ahead to play. I think he can really do a lot for our younger defensemen," Regier said.
Regehr, 31, was an alternate captain for the Flames, with two goals and 15 assists in each of the past two seasons. He'll bring some grit to the blue line, with the Sabres aggressively trying to upgrade their roster under the new ownership of Pegula.
Regier said he expects Kotalik, 32, who played with the Sabres from 2001-02 to 2008-09, to compete for a roster spot at training camp. He said there were no plans to buy Kotalik out of the final year of a contract that pays him $3 million.
Information from ESPN.com's Pierre LeBrun and Scott Burnside and The Associated Press was used in this report.