The 35-year-old has opted to leave Benevento after just five months with the Italian club, with whom he suffered relegation from Serie A at the end of 2017-2018.
Sagna was without a club after leaving Manchester City in June 2017 after a three-season spell in which he helped club to a League Cup win in 2015-2016.
Montreal has the option of signing Sagna for a further year and the right-sided defender, who earned 65 caps with France between 2007 and 2016, joins a team currently fifth in the Eastern Conference.
Impact head coach Remi Garde told the club's official website: "I'm very happy of Bacary's arrival.
"He's a player with a great career who's still very motivated to come and help the Impact defy its end of season challenge.
"His personality, experience, and overall game will be a plus for our team."