Saturday’s 3-1 home defeat to Preston North End proved the final straw for the club, who announced the decision shortly after full-time.
Leeds 5/1 to win Championship
Redknapp was appointed in April and helped the Blues narrowly avoided relegation from the second tier last term.
But they now sit just one spot above bottom-placed Bolton and have lost six straight matches in all competitions.
Former Everton midfielder Lee Carsley, part of Redknapp’s backroom staff, will takeover as caretaker manager.