The 70-year-old Englishman’s appointment comes 16 hours after Zola resigned following a 2-0 defeat by Burton Albion.
Redknapp will initially take charge of the Blues until the end of the season.
Birmingham are 20th in the table, three points above the relegation zone with three games left, after a run of just two wins in 22 league games under Zola.
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“Birmingham are a proper football club but they are in a precarious position,” Redknapp, 70, told Talksport.
Redknapp’s tenure at the club gets underway on Sunday with a trip to local rivals Aston Villa before hosting Huddersfield Town and finishing off the season away at Bristol City.