The Spanish international has scored seven goals in his first four games for the Blues and netted a hat-trick in the 4-2 win over Swansea City at the weekend.
"Chelsea spent an awful lot of time and money trying to replace Didier Drogba. It looks like they have finally found their man," former Premier League midfielder Redknapp is quoted as saying by the Daily Mail.
"What more can you say about Diego Costa? He has arrived in the Premier League and is probably thinking: 'Everyone is scared of me and I've got Cesc Fabregas to supply the bullets.' He must be absolutely loving it.
"He has seven goals in four games — it took Drogba 18 games to match that — and Costa is the complete package, scoring with both feet and his head. He is the real deal."
Costa joined Chelsea from Atletico Madrid for a reported fee of £32m in July.