Remy underwent an Rs medical last night.
Redknapp said: "Remy had a medical today and the personal stuff is all sorted.
"I watched him so many times when I was at Tottenham. The fee then was around about £20million. He's a good buy for us.
"It's all done, all sorted. I didn't think we'd get him. I went to see him at Marseille last week and he wasn't keen but the chairman Tony Fernandes worked ever so hard. He wouldn't give up and the boy decided to come.
"He's quick, a French international, his movement is excellent and he has the potential to be a real star in the Premier League.
"Newcastle United wanted him and Graham Carr (chief scout) doesn't make too many mistakes. Graham's got good judgement."