The Netherlands international follows Spanish winger Ferran Torres to the Etihad Stadium as Pep Guardiola looks to refresh his squad.
Manchester City have completed the signing of Bournemouth defender Nathan Ake in a deal worth an initial £40 million ($53m).
The deal represents a club-record transfer fee for Bournemouth, who could receive a further £1m ($1.3m) in add-ons for the Netherlands international.
Goal reported last week that the two clubs had agreed terms, and the 25-year-old has since returned from an end-of-season break to complete his medical and sign his new contract in Manchester.
Ake started his career at Chelsea, and the west London club did have a buy-back option, but it is understood that they were put off by the fee despite Frank Lampard considering him as a viable option.
“Coming here is a dream for me. This is a top side full of world-class players. Everywhere you look in this squad there are big names with international pedigree.
“Pep 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.
“I know I’m going to have to work hard to get into the side, but that’s what I’m here to do. I’ll do whatever I can to make an impact and help the team win silverware.”
City have been in the hunt for a new central defender since the exit of captain Vincent Kompany in June 2019. They were interested in Harry Maguire but balked at the asking price for the England international, who eventually joined Manchester United in an £80m ($97m) deal last year.
Despite Bournemouth’s relegation to the Championship, Ake’s reputation has soared since he left Stamford Bridge in 2017. As well as being a homegrown player, he has experience of playing regularly in a back-three and can also provide cover at left-back.