The 37-year-old winger, a two-time Copa America champion with Chile, has also made stops at Manchester United, Inter Milan and Marseille and spent last season with Sevilla in La Liga.
"I'm very happy to join CF Montreal and take on this new challenge," Sanchez said. "I'm grateful to the club for the confidence they've shown in me and I'm eager to put my experience to work so that we can reach our objectives and create memorable moments for our supporters."
With four wins and four draws from 18 MLS matches, Montreal sit 14th in the 15-team Eastern Conference and are third-worst in the league overall, with only Atlanta and Kansas City trailing.
CF Montreal senior director Luca Saputo hopes the deal, which has a club option for the 2027-28 season, will begin a turnaround for the Canadian club.
"The arrival of Alexis Sanchez represents an important step in our sporting project," Saputo said.
"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."
Sanchez helped Arsenal take the 2015 and 2017 FA Cups and won Serie A titles with Inter Milan in 2020/21 and 2023/24, plus two Supercoppas and an Italian Cup.
He helped Barcelona win the Spanish Super Cup, UEFA Super Cup and FIFA Club World Cup, plus a Copa del Rey and La Liga crown.
With Chile, Sanchez helped land Copa America titles in 2015 and 2016.