The addition of the decorated frontman comes at a pivotal time for Montreal, who sit 14th in the Eastern Conference after taking just 16 points from 18 matches under interim manager Philippe Eullaffroy.
Montreal chief Luca Saputo warmly welcomed the high-profile arrival: "The arrival of Alexis Sanchez represents an important step in our sporting project. Alexis possesses exceptional technical quality and experience at the highest level of world football.
"His personality, leadership and competitive mindset fully align with our club's identity and ambitions. We are of firm belief that he will have an immediate impact both on the field and in the locker room."