The French Ligue 2 team, which is owned by the City Football Group, had previously loaned out the talent to another City-owned side.
Savinho impressed at Girona in La Liga last season, helping them reach the Champions League.
City Director of Football Txiki Begiristain stated: “Savinho is a very exciting player and I think the City fans are really going to enjoy watching him.
“What he achieved last season at Girona was remarkable and he is already a full Brazil international. He has a big role to play for Manchester City this season and beyond.
“We are totally confident in his ability. He is still young and has the potential to become even better, and everyone knows that Pep is the best at helping players develop even further.
“But he has already shown his huge quality and technical ability and is an exciting addition to our attacking area.”