The former Spain international, 34, has left City after a decade of service in which he won 11 major trophies including four Premier League titles. The Manchester outfit had announced earlier on Monday that they would be honouring the Spaniard by building a statue of him outside the Etihad Stadium.
La Real, who finished sixth in La Liga, were searching for a new playmaker after Martin Odegaard ended a one-year loan spell to return to Real Madrid. Silva had been linked with a move to Italian club Lazio, but instead returns to his home country, having begun his professional career at Valencia.
In a social media post, Silva said goodbye to Man City fans:
"I look back and it's clear I could not have made a better decision than to accept City's proposal to join their project back in 2010," he said.
"Manchester City and I have grown together. In 10 years, I have developed personally and professionally. I have celebrated many victories and titles and lived through epic moments.
"I have seen my lovely child, Mateo, born and I have even started to feel comfortable under heavy rain! City are a fantastic family. I won't ever forget the way they threw themselves into helping me when I suffered the hardest moments of my life, offering me support and empathy."
To help fill the void following Silva's departure, City have signed Ferran Torres from Valencia in a deal worth €23 million plus add-ons. City have also signed centre-back Nathan Ake from Bournemouth in a deal worth £41m.
City's summer recruitment has been made more simple after their two-year European ban was overturned by the Court of Arbitration for Sport, but privately club bosses insist it does not mean there will be a blank cheque for new players.
Information from Reuters was used in this article