The 26-year-old has agreed a four-year contract with City after the two Premier League clubs settled on an undisclosed fee.
And Ben Haim admitted Mark Hughes influenced his decision to opt for Eastlands.
"I think it's a very good club and a famous club with a lot of ambition," he said. "I want to win things with this club and I know for many years that hasn't happened. It'll be hard and it takes time to build something.
"I know Mark Hughes matches my ambition. As a player he won nearly everything and of course he wants to do the same as a manager.
"He has ambition, the passion and the desire to do that and it matches my ambition because I am like that as well. I want to help City to be a better club and to win something."
Ben Haim also told the club's official website that he turned down the advances of other clubs to sign on at City.
He said: "I spoke with my agent and even though we had some better offers I preferred to come here because I think it's a good club with a lot of ambition. As I've said, we want to do better things here than over the last few years.
"There were a few other clubs, but after I spoke with the staff here and my family, I think it's the right club to try to build something new.
"There were some from abroad as well, but I preferred to stay in England."
Ben Haim added: "I'm definitely going to give my best to City and give my heart in every game.
"I hope that we can do good things this season. I'm looking forward to starting the season here."