City signed the Wolfsburg striker in the early hours of this morning for £27 million.
Dzeko is likely to make his debut against Wolves at Eastlands on January 15.
He told the club's official website: "It has been a long time that I have been linked with the club going back to last summer but Wolfsburg did not want to sell me until today.
"There was too much speculation in the papers but my head is always clear. It is important that is the case because if you think too much about what might be it is a distraction and it can affect your game. I was always attracted most to joining City.
"They have been playing well this season. I have watched them a lot on television. Now the speculation is over and I just want to do my best."
Bosnian star Dzeko, who has most recently been on a winter break with former club Wolfsburg, has no doubt why he joined the Blues.
He added: "Everybody speaks about City having lots of money but it is not about that. It is about ambition and I have spoken to coach Mancini and he told me 'this is the best club for you'.
"City are playing for first place in the Premier League and that is what I want. I am excited to play alongside players such as Tevez and Toure who I have only seen on the television and to be in the same team as players I have played against such as Boateng and Kompany.
"They will help me achieve my goal to be better in the future. I want to show the fans why the club paid the money for me. Everyone expects goals and I want to score them but most of all I want to contribute to a successful team.
"I don't want to talk about my skill - that is for other people to judge. However, I know my quality and when I am fit I am not afraid of a challenge.
"I don't know a lot about Manchester because I have only been once but I am looking forward to seeing the city and meeting the fans and getting to know everyone at the club."