The Midlands club dismissed former boss Steve Cotterill on Saturday evening after they lost 2-1 against Nottm Forest. That result left the relegation-threatened side 22nd in the Championship.
Monk will be joined at Birmingham by Pep Clotet, his assistant from his time at Leeds, Jamis Beattie and Darryl Flahavan, both also with him at Elland Road.
Monk managed Swansea and captained them to a League Cup win in 2013.
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