The Netherlands centre-back has signed a five-year contract with his new club.
The news comes just a day after City secured the £21m signing of Ferran Torres from Valencia.
“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. 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."
We're excited to announce the signing of @NathanAke from Bournemouth on a five-year deal
#ManCity | https://t.co/axa0klD5repic.twitter.com/6tyYQ2OVwv
— Manchester City (@ManCity) August 5, 2020