The Championship (second tier) side said the 60-year-old had agreed terms on a two-and-a-half-year deal and would take training for the first time later on Monday.
He will be Birmingham's third manager of the season, with John Eustace making way for Rooney in October.
Mowbray was previously in charge at rivals Sunderland, taking them to the promotion playoffs last May but being fired in December.
He has also managed Blackburn Rovers, West Bromwich Albion. Middlesbrough, Coventry City and Celtic and Hibernian in Scotland.
"Tony was the standout candidate in our search for a new manager. His knowledge of and passion for the game shone through," said City co-owner and chairman Tom Wagner in a statement.
"He shares our ambition and will bring stability at an important time for our great club. We received extremely positive feedback from everyone we spoke to about Tony."
Birmingham were sixth when Rooney was appointed but had slumped to 20th, six points above the relegation zone, when he was sacked after winning just two of his 15 games in charge.
