The 25-year-old Dutchman was relegated with the Cherries in 2019/20 but is making an immediate return to the Premier League, joining the four-time champions.
He follows hot on the heels of Spanish winger Ferran Torres, who completed his own move to Man City from Valencia on Tuesday.
“City have been the best side in England over the course of the last decade,” Ake told City's official website. “Coming here is a dream for me. This is a top side full of world-class players.
“Pep [Guardiola] is a manager admired across the world – what he’s done in the game speaks for itself. The success he’s had is unbelievable and the style of football he plays really appeals to me."
Ake will bolster a Man City defence that conceded 35 goals in 2019/20, 12 more than in their 2018/19 title-winning campaign.
In addition to his defensive prowess he also boasts a goal threat from set-pieces, scoring 12 times and adding six assists during his Premier League career so far.