The 35-year-old, most recently on the books of Serie A strugglers Benevento, must first complete a medical before his free transfer can be finalised.
Sagna is to link up with ex-Aston Villa manager Remi Garde in Canada, with an option in place to stay on for the 2019 season if he impresses over the remaining months of this campaign.
Garde told Montreal's official website: "I'm very happy about 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."
Technical director Adam Braz added: "We are very happy to welcome Bacary to the club.
"Bacary brings a wealth of experience at the highest levels of the game and that will be invaluable to the team during our last stretch of games in the regular season and in our quest to make the playoffs."
Sagna won the FA Cup and EFL Cup during his decade in English football.