City agreed a £40million fee, rising to a potential £41m, with the relegated Cherries last week and the 25-year-old has signed a five-year contract.
Ake is City’s second signing of the delayed summer transfer window, after the club landed Spain Under-21s winger Ferran Torres from Valencia.
With Aymeric Laporte missing five months of the current season through injury and Guardiola appearing to lose faith in a John Stones-Nicolas Otamendi partnership, midfielder Fernandinho often played as a makeshift centre-back.
Ake comes to the Etihad to strengthen City’s options at the back.
Ake was a youth player at Chelsea and had loan spells at Reading, Watford and Bournemouth before joining the Cherries permanently for £20m in 2017.
Chelsea reportedly had a buy-back option but chose not to exercise it.