Redknapp revealed his disappointment with Chimbonda signing 15 minutes too late, denying him the chance to play in Tuesday's home Premier League game against Stoke.
"He's a player I've always liked when he was at Tottenham before," Redknapp added.
"He plays with energy, he gets forward, he's a great attacking full-back.
"He was in the team of the year in the Premier League a couple of years back. I'm pleased to have him here. I tried to get him when he was at Wigan."
Chimbonda only lasted one season with Wigan before his form at right-back prompted Tottenham to seal his signature in 2006.
After a promising start at the Stadium of Light, he lost his place in the side under former manager Roy Keane, but had been showing a return of form, having started the last four games for Sunderland.
Black Cats boss Ricky Sbragia revealed earlier on Monday that Chimbonda had struggled to settle at the club and said: "We had an opportunity to maybe make things a little bit happier for him."
Tottenham also signed the 35-year-old Chelsea goalkeeper Carlo Cudicini on Monday, on a free transfer.
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