In exchange, the Sabres gave up a second-round pick in the 2016 draft in a deal made Tuesday shortly after the start of the NHL's free-agency period.
Gorges is a nine-year NHL veteran, who spent the past seven-plus seasons in Montreal. He's a dependable blue liner, whom the Sabres targeted to help groom their young crop of defenseman.
He had a goal and 13 assists in 66 games last season, and has 14 goals and 84 assists in 560 games.
The Canadiens quickly filled the void left by Gorges by agreeing to sign free-agent defenseman Tom Gilbert to a two-year contract.
Gilbert is an eight-year NHL veteran who spent last season with the Florida Panthers.