The Rs moved quickly to get their man, having begun talks with the former Tottenham boss on the same day as firing the Welshman. The 65-year-old will watch Saturday's game against Manchester United from the stands before taking charge on Monday.
"I'm delighted to be back in the managerial hotseat at QPR. I can't wait to get started," Redknapp told the club's official website.
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"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."
The Rs are still searching for their first win of the season, with only four points from their first 12 league games, but Redknapp has experience in turning clubs around, with the Englishman establishing Tottenham as a top-four team after taking over in 2008 when the club had two points from eight matches.
QPR chairman Tony Fernandes declared: "Harry was our No.1 target, the unanimous choice of the board, and we're delighted we've been able to attract him to the club.
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"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.
"We believe we have a manager with significant experience at the highest level of football, who can come in and immediately help deliver our objectives."
QPR shareholder Kamarudin Bin Meranun added: "While we look forward with Harry we would also like to place on the record our appreciation to Mark."