Sherman was the head coach at Texas A&M from 2008-2011, and Manziel was offered a scholarship from his staff and spent his freshman year learning from Sherman in 2011.
Although he hasn't played since 2015, Montreal felt strongly enough about Manziel to surrender two future first-round picks to Hamilton in the five-player deal.
Manziel, 25, made headlines across North America when he signed a two-year contract with Hamilton prior to the start of training camp.
The Alouettes wasted little time promoting their acquisition of the former Cleveland Browns quarterback and Heisman Trophy-winner.
And that prompted some football pundits to suggest it was time for Manziel to get some playing time with Hamilton. "Landon Rice and Tony Washington are two skilled players that will considerably solidify our offensive line".
The addition of Manziel comes a day after Alouettes starting quarterback Drew Willy left Saturday's 25-8 loss to the Calgary Stampeders with a hand injury. Montreal was already without quarterback Jeff Mathews for four to six weeks because of a foot injury.
Montreal (1-4) hosts Edmonton on Thursday night.
"We have acquired an exceptional quarterback with undeniable talent", said general manager Kavis Reed in a statement. "With his great mobility, his athletic abilities and his instinct we believe that he will have a positive impact on our offence".
Sherman and the Alouettes have the scored the fewest points in the CFL this season. He made a two-year commitment to the CFL in May, but if Manziel can re-establish himself as a capable quarterback, he might find his way back to the National Football League in 2020.
The Tiger-Cats are 2-3 this season, which puts them in second place in the East Division.