Redknapp installed McClaren to his coaching staff last summer, but the former England manager would depart for the Rams in September following the sacking of Nigel Clough.
"I’m delighted that he came in and he was great when he was here,” Redknapp said.
“I always knew he was going to go off and work somewhere else at some point. And when the opportunity came with Derby it was a job he could not resist.
“It was a club that he played at, been assistant manager there alongside Jim Smith and when the chance came he had to take it.
“He has done a great job.”
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