Rooney left his role as DC United manager in America's Major League Soccer on Sunday after they failed to reach the playoffs.
Birmingham sacked previous manager John Eustace on Monday after 15 months in charge.
Former England left back Ashley Cole and ex-Manchester United defender John O'Shea will be part of Wayne Rooney's coaching staff at the Saint Andrews' Stadium.
Birmingham City are currently sixth on the Championship table.
Following his appointment, Rooney, who has also managed Derby County, said: "I am absolutely delighted to be joining Birmingham City Football Club at such an exciting time. It is very clear that they have a plan and are committed to realising their ambition for the club. We are fully aligned on what is expected.
"I have been building my managerial career, putting myself in challenging environments, to get me ready for this opportunity. It's a project that gives me a sense of purpose and I can't wait to get started.
"We have some exciting young players in the squad, and some who are still to break through into the first team, alongside a core of experienced senior professionals. I have a clear way that I want the team to play, and my coaching staff and I will work hard to implement it. We will create a winning culture here with an identity that gets Blues fans on their feet.
"I've played at St. Andrew's and Birmingham City fans were always loud and passionate about their team. It was a really difficult place to come as an opponent and now I get to experience what it is like to have them behind us.
"My job is to elevate the club to the next level and I can't wait to get started. I know what the expectations are and our job is to deliver."
Rooney's first game in charge of Birmingham will come against Middlesbrough after the international break.
