The 65-year-old revealed QPR’s latest transfer activity after the west Londoners were 1-0 winners against West Bromwich Albion in their FA Cup third-round replay on Tuesday.
“Remy has had a medical today, so that’s all sorted,” Redknapp told BBC Sport. “M’Vila, I think we’re very close.”
Redknapp has been a long-term admirer of Remy, but Mark Hughes’ successor appeared to have given up all hope of signing the Marseille striker last Friday.
The QPR manager revealed that Remy would not even meet with him to discuss a potential move, but it appears owner Tony Fernandes has successfully convinced the France international to complete a touted £8m switch to Loftus Road.
“Remy is a good player,” he added. “Newcastle do very well in the French market as well with Graham Carr their chief scout, and he is a boy I looked at an awful lot while I was at Tottenham.
“Last year we were talking about paying £20m for him. We looked at him, we liked him and we were chasing him but didn’t quite 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.”
Redknapp also confirmed that QPR have made an offer, reported to be £7m, for Rennes’ M’Vila – and the Hoops boss is confident the France international would be a valuable addition to his squad despite the midfielder’s controversial past.
“He played against England a couple of years ago for France, and was fantastic,” Redknapp said.
“Rennes turned down £28m from an English club for him a year ago. Spurs offered £15m for him in August. The deal looks OK.
“M’Vila’s had a few off-the-field problems. If he behaves himself, and plays as we know he can, he’ll do well.”
“The type of money hopefully we can pull off two deals for is fantastic.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news