City have reached agreement with the 24-year-old's Spanish club Valencia, who confirmed the move, pending a medical.
Spanish media reported the deal was worth about 32 million euros although no financial details were given in the announcement on City's website.
"The player's advisers and officials from both clubs have finalised the details... he will complete his medical and officially become a City player once his involvement in the World Cup is over," the world's richest football club said.
The pacy left-footer has been a potent force at Valencia and at international level with team-mate David Villa, Spain's goalscorer in their World Cup second-round victory over Iberian neighbours Portugal on Tuesday.
"The time is right for me to seek a new challenge, and I am thrilled about playing in England with Manchester City," the City website quoted Silva as saying from Spain's World Cup base in South Africa.
"I believe the Premier League is one of the best competitions in the world and I want to bring success to City and win trophies for them."
City's Italian manager Roberto Mancini said Silva was an important signing for the Abu Dhabi-owned club who finished fifth in England last season to qualify for the Europa League.
"I think that David Silva is one of the best midfielders in Europe," he said.
"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," added Mancini.
After selling top scorer Villa, Valencia president Manuel Llorente had warned there would probably be more sales, saying: "The board's principle objective is to make sure we have economic viability for the future."
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