The 25-year-old, who was also linked with Liverpool, has signed a five-year deal with City.
The Argentine has spent the last two seasons on loan with Manchester United, but turned down the chance to sign a deal with the club.
“It is terrific news,” City boss Mark Hughes told the club’s official website. “Carlos is an international player of the highest class who possesses all the attributes that will help drive this club forward.
“He is not only outstanding technically, but he is a reliable goalscorer and someone who will contribute fully to the team ethic. He gives us another exciting, attacking dimension.
“I cannot wait to welcome him to City. This is yet another deal that shows the commitment of the owner Sheikh Mansour to make this club the very best it can possibly be. I am sure our fans will give Carlos an exceptionally warm welcome.”
