Dunne moves to QPR on a free transfer.
Redknapp enthused about the quality possessed by Dunne but also admitted if his recent injury problems return the club retain the right to cancel the contract.
"This is a great signing for us," Redknapp said.
"He's a top-class defender and a great guy. He's a good character and just what we need.
"He was City's Player of the Year four years running, and he will be fantastic at this football club. He's exactly the type I'm looking for.
"Obviously he had his problems last season with the injury but there's an agreement in place that if he breaks down, the contract can be ended. He's confident he'll be okay and from our point of view, if he doesn't have any problems with it then we've just signed a very, very good centre-half."