The 19-year-old joined City from Italian side Fiorentina on transfer deadline day.
“I’m so happy, I just can’t put it into words,” Nastasic told Mondo.
“I have become part of a great club. Manchester City are going places and I’m now part of it. It feels truly great.
“I was really surprised when City called me and then everything happened so quickly I couldn’t believe it. I’m living my dreams.”
He added: “I hope that I will not need a lot of time to adapt but I know that it is not the same to play in Italy as England.
“This is a big step ahead in my career. I’m only 19 years old.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?