Ylonen was assigned to AHL Syracuse on Sunday.
Ylonen signed a one-year, $775,000 contract with the Lightning on Monday, per Eduardo A. Encina of the Tampa Bay Times.
Ylonen won't receive a qualifying offer from the Canadiens, per Arpon Basu of The Athletic on Thursday, which will make him an unrestricted free agent Monday.
Ylonen scored a goal on one shot in Thursday's 4-1 win over Philadelphia.
Ylonen remains pointless in 19 straight matches, leading to him being scratched against Boston on Thursday, Arpon Basu of The Athletic reports.
Ylonen (undisclosed) is in Wednesday's lineup against the Devils, per the NHL's media site.
Ylonen recorded an assist and one shot on net over 11:36 of ice time in Saturday's 4-3 shootout win over the Rangers.
Ylonen had an assist and finished plus-2 over 12:30 of ice time in Friday's 5-2 win over Chicago.
Ylonen had an assist over 7:26 of ice time in Wednesday's 4-3 shootout loss to the Penguins.
Ylonen had one shot on net and scored the winning tally in the shootout of Friday's 3-2 win over San Jose.