Fortier, who was set to become a restricted free agent this summer, inked a one-year, two-way contract with Tampa Bay on Wednesday.
Fortier was assigned to the minors Monday by the Lightning, according to Erik Erlendsson of LightningInsider.com.
Fortier worked in with the offensive lines through practice on Tuesday and looks set to make the Lightning as the 13th forward, reports NHL.com.
Fortier was demoted to AHL Syracuse on Tuesday.
Fortier was called up from AHL Syracuse on Monday.
Fortier agreed to terms on a three-year, entry-level contract with Tampa Bay on Wednesday.
Fortier was drafted 59th overall by the Lightning at the 2018 NHL Entry Draft on Saturday.