The terms of the deal give City a 44.3% share of the club, an identical holding to Girona Football Group, the agency owned by City manager Pep Guardiola's brother, Pere. The remaining stake is owned by a Girona fans' association.
After achieving promotion last season, Girona are playing in La Liga for the first time in their 87-year history, having reached the play-offs in three of the last four seasons.
City have already had close links with the Catalan team, sending them five players on loan this summer: Pablo Maffeo, Aleix García, Douglas Luiz, Marlos Moreno and Larry Kayode.
A statement which announced the agreement said Girona would “benefit from City Football Group’s extensive networks in infrastructure, coaching, recruitment, youth development and executive leadership in addition to its global media, marketing and commercial capabilities”.
Ferran Sorriano, City Football Group's CEO said: “Girona is a club whose actions have spoken loudest in terms of its ambitions. It has quietly and with great determination and humility achieved promotion to La Liga which is, itself, an incredible achievement. It has also done so whilst playing good football.
“The club’s continued ambitions to achieve sustained La Liga status and success while applying those same qualities and behaviours is an ambition we share at City Football Group and the opportunity to invest in the future of Girona was compelling. We will listen and learn, and do whatever is necessary to support the club and its fans in achieving the long-term sustainability they rightly desire.”