Speaking at a news conference, the 24-year-old said: "I hear a lot about the fans - that most of the people from Manchester are City fans."
Premier League leaders United are two points ahead of City in the table, with two games in hand.
Since billionaire Arab tycoon Sheikh Mansour completed his takeover in 2009, City's spending has eclipsed that of their local rivals.
He is different from the other players we have. Now we have a good mix. I hope he can score a lot of goals like in Germany
City manager Roberto Mancini
City also angered United in the summer of 2009 by displaying a "Welcome to Manchester" poster on completing the transfer of Carlos Tevez from his advisors, the Argentine striker having spent the 2007-08 and 2008-09 campaigns on loan at United, who had deemed an asking price of £25m to be excessive.
United manager Sir Alex Ferguson retorted by branding City a "small club" while later describing them as "noisy neighbours" after his side's controversial 4-3 derby victory in September 2009.
Dzeko's signing is further proof of City's financial clout and the striker added that he was relishing the prospect of playing for a club he believes are well equipped top match his own ambitions.
"I saw something else in Man City. It's a big club and I'm an ambitious player and I think we can have a lot of success together," he continued.
"It's a project. I need to say it's a very good team with a very good coach. It was three-and-a-half beautiful years with Wolfsburg and we had a lot of success, winning the league for the first time in our history.
"I was very happy there but I wanted to change, try something new and better and that's why I'm here."
I am delighted about Edin's arrival I think as he is amongst the best target men in the world
City manager Roberto Mancini hailed the signing of the Bosnian international, who has scored 66 goals in 111 games in Germany, including 10 goals in 17 league games this season.
"I am very happy the club bought Dzeko," Italian Mancini stated. "I think he'll be a very important player for the future of this club.
"We wanted him in the summer because we knew he was the perfect player for us. He is different from the other players we have. Now we have a good mix. I hope he can score a lot of goals like in Germany.
"I think we spoke with him six months ago for the first time. We wanted to know if there was a chance to buy him but we do this now in January.
"It's important because now we are in a good position in the league. With one player like him we can improve in the Barclays Premier League and the Europa League. We have more chances in this moment."
Although Dzeko's signing is expected to trigger the departures of fellow strikers Emmanuel Adebayor and Roque Santa Cruz, the Bosnian will still form part of an impressive forward unit available to Mancini, alongside Jo, Mario Balotelli and Tevez.
Source: BBC Sport
Source: BBC Sport