The 24-year-old has agreed to a five-year contract with the Premier League side.
The Spain international will complete a medical at Eastlands and join City after the World Cup.
City boss Roberto Mancini said: “I think that David Silva is one of the best midfielders in Europe, and I hope he will be a very important player for Manchester City.
“I am so pleased he is coming to us, I think he can make a big, big impact for Manchester City.
“In signing David, we are showing the world that we are bringing the best players here and that we hope to compete to win the Premier League.
“When players see what is happening at Manchester City and the ambition they are attracted to what we are building and want to be a part of it.
“I hope he does very well for Spain in the World Cup and then joins us for our pre-season, ready to compete in the Premier League.
“I am very excited about seeing him playing for Manchester City.”
