Troyes have become the 10th club purchased by the City Football Group (CFG).
CFG owns Manchester City and is backed by the Abu Dhabi United Group, which was formed to buy the Premier League outfit in 2008.
The group also has stakes in New York City, Melbourne City, Yokohama F Marinos, Montevideo City Torque, Girona, Sichuan Jianiu, Mumbai City and Lommel SK.
Its latest acquisition is Troyes, who finished fourth in Ligue 2 last season.
The French outfit have bounced between the top two tiers in recent seasons, most recently suffering relegation in 2018, having played in the UEFA Cup - now the Europa League - after the turn of the century.
Troyes were reportedly the subject of interest from Olympiakos and Nottingham Forest owner Evangelos Marinakis earlier this year.
CFG managing director Ferran Soriano said: "We have been interested in French football for some time and have long admired ESTAC.
"We are therefore delighted to have completed the acquisition of our 10th club and to have a permanent presence in France.
"This is an important milestone for City Football Group, which proves that our model continues to adapt and develop in a relatively short period of time."