Savinho shone last season on loan at Girona, another club owned by the City Football Group (CFG).
City will reportedly pay a fee of 40 million euros (£31m, $44 million) for the 20-year-old, who has signed a five-year contract.
Despite being registered to the Ligue 2 club, Savinho never played a minute of action for Troyes.
After his signing from Atletico Mineiro in 2022, he was immediately loaned to PSV Eindhoven.
The Brazilian international then spent the last 12 months in La Liga, where he scored nine goals and provided 10 assists as Girona finished third behind Real Madrid and Barcelona to qualify for the Champions League for the first time in their history.
“Everyone knows they are the best team in the world right now, so to be here is very exciting for me,” said Savinho in a City club statement.
“I’m excited about the chance to work under Pep Guardiola, one of the greatest coaches ever, and someone I know will help me improve even more.
“I had an amazing time in Spain and I’m looking forward to a new challenge of playing in the Premier League and alongside some of the best players in the world.”
However, the nature of the deal will raise further questions about the fairness of multi-club ownership structures.
CFG have stakes in 12 clubs in five different continents around the world.
Earlier this month UEFA green-lighted City and Girona to both play in the Champions League, as well as Manchester United and Nice, who are both controlled by British billionaire Jim Ratcliffe’s Ineos company, in the Europa League.
© Agence France-Presse
Photo: Bagu Blanco / Pressinphoto / Icon Sport