The 32-year-old Hutton has six seasons of NHL experience, including the past two with the Blues, where he split starting duties with Jake Allen. He finished with a 17-7-3 record and a 2.09 goals-against average in 32 games last year.
The Sabres have needs at goalie after electing not to re-sign third-year starter Robin Lehner and veteran backup Chad Johnson.
Hutton will form a tandem with Linus Ullmark, who is pegged to make the jump to the NHL level on a full-time basis after spending the past three years developing in the minors.
"Carter is a great fit for our young Sabres team," Sabres goaltending coach Andrew Allen told the team's official website. "Our team is in an exciting building stage and Carter will bring character, experience and the ability to win games to our group, all the while competing to continue to earn his starts both in practice and through game results.
"Carter will be an ideal partner for Linus Ullmark -- to communicate with, learn from and create healthy competition. Playing with Pekka Rinne for multiple years taught him a lot about how to be successful in the NHL and he will pass this on to Ullmark through the way he goes about his business every day."
The Associated Press contributed to this report.