The MLS outfit confirmed the Argentinian midfielder's departure about an hour after San Lorenzo celebrated the beginning of Piatti's second stint by tweeting a video. He won the Copa Libertadores during his previous stay with the Buenos Aires club.
"I would like to thank Nacho, personally and on behalf of our club, for his six years with the Montreal Impact," Impact owner and chairman Joey Saputo said. "His professionalism, class, and love for the sport, this club, and this city have marked his time in Montreal.
"The thrilling moments he allowed us to experience and share through his play on the field will remain fixed in this club's history, as will his status as one of the greatest players to wear the Impact jersey."
Piatti joined Montreal in July 2014 and went on to make 135 MLS appearances for the Quebecois side. The three-time All-Star was named Montreal's Most Valuable Player for four consecutive years (2015-18) and leaves as the club's all-time top scorer with 78 goals in all competitions.
"I wish Nacho all the best in his return to his homeland and look forward to welcoming him back as an alumnus once his playing days are over," Saputo added.
The 35-year-old helped Montreal reach the CONCACAF Champions League's two-legged final in 2015 and the MLS Eastern Conference final in 2016.