Redknapp has only three games to save Birmingham from the dreaded drop out of the Championship, with the defeat to Burton leaving the free falling Blues three points above the relegation zone.
Former Chelsea forward Zola previously managed West Ham United and Watford in England but managed just two wins in 24 matches at Birmingham.
In 2008, Redknapp was appointed Tottenham boss and was at White Hart Lane for four years, qualifying for the Champions League in 2009-10.
Harry Redknapp, one of English soccer's most charismatic coaches, was back in management at age 70 on Tuesday when he was hired by relegation-threatened second-tier team Birmingham.
Redknapp's brief does not now extend beyond securing Birmingham's second-tier survival but if he can achieve that aim, he could be convinced to remain in charge for a crack at promotion to the Premier League.
Zola stood down on Monday, declaring "I sacked myself".
The Blues were seventh in the division when the Italian controversially replaced former boss Gary Rowett.More news: New Zealanders Are Bracing For The Worst Storm In 50 Years
Steve Cotterill will also be part of the backroom staff when Redknapp begins his appointment which is to be at the end of the season.
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. "Now I've got a slightly bigger problem".
'They are in a precarious position and we've got the worst goal difference as well.
"My wife said to me 'are you mad or what?' but I get fed up sitting around doing nothing".
More recently, Redknapp was briefly in charge of Jordan for two World Cup qualifiers a year ago and was also working as an advisor to Derby County last season.
"I was anxious how I was going to find a centre half among the jockeys with them all being so small. If I feel like I can not help these players why stay - it's better that I leave and let somebody else do that".