Cotterill was assistant to Redknapp at St Andrew's for the final few games of last season as the pair kept the club in the Championship, before turning down the chance to remain in the role.
Redknapp was subsequently sacked by the Blues last month following a poor start to the campaign, with Cotterill taking over in the veteran manager's place.
"I've been a manager for many years now and I wanted to be that again in my own right," Cotterill told Sky Sports News. "It was 100% nothing personal with Harry or anything like that.
"The fact it's happened here, I wouldn't have known what the odds would have been on that, but it's a pleasant surprise. I'm saddened it didn't work out for Harry for sure, and I never thought I'd be coming back here [as manager]. It's been a freak situation how it's happened.
"But I'm delighted to be back, it's a fantastic club that is supportive and friendly, and we're looking to get some wins on the board and put some smiles on a few faces."
Cotterill's first game in charge of Birmingham will be at home against Cardiff City on Friday night.