The former Tottenham boss has replaced the sacked Mark Hughes at Loftus Road on a two-and-a-half year deal.
Redknapp: "I'm delighted to be back in the managerial hot-seat at QPR.
"When I spoke to the shareholders and they told me about their plans I knew this was too good an opportunity to turn down.
"There's no doubt there's a lot of ability in the squad, but for one reason or another things haven't gone as well as everyone expected since the start of the season.
"I can't wait to get to work and get the results necessary to kick-start our season."
QPR chairman Tony Fernandes: "Harry was our number one target, the unanimous choice of the board and we're delighted we've been able to attract him to the club.
"He has a proven track record in the Premier League and has all the characteristics we were looking for to get us out of the current situation we find ourselves in.
"His man-management skills are second to none and we are confident he is the right man to lead us away from the bottom of the table."
One problem Redknapp will face - will he try and keep hold of former Toon skipper Joey Barton, who is currently out on loan in France.