Silva, who was a member of Spain's World Cup winning squad, underwent a medical on Wednesday and has put pen to paper on a four-year contract at Eastlands
"I'm very happy with what we did this summer, it's the best time that any player can have," Silva told the club's official website.
"I am looking forward to starting the season with my new team, I'm excited about my new team.
"And I will be happy if at the end we are in the Champions League - or if we win a trophy.
"Roberto Mancini and Garry Cook have told me we are building a very good team with some of the best players in the world and we are going to fight for honours.
"My first target is to get into the team, and then to fight for the league and the other competitions."