The 18-year-old winger has had a breakthrough season in Ligue 2, contributing two goals and six assists in 29 appearances.
Troyes are currently top of the second division and on course for promotion to Ligue 1, and the plan is for Detourbet to remain at the club on loan next season before moving to the Etihad in the summer of 2027.
Both clubs are part of the City Football Group, which simplifies the mechanics of the deal considerably. Sporting director Hugo Viana has been personally involved in negotiations.
Roma had previously submitted a formal offer of around €10 million for the French Under-19 international, and AS Monaco and several Bundesliga clubs were also monitoring him, but City's structural advantage has proved decisive.
Detourbet is a left-footed winger who has drawn attention for his technical ability and directness at a young age.
The loan-back arrangement mirrors the approach City have used with other CFG signings, most notably Savinho, who came through Girona before establishing himself in Manchester.