It was originally believed the club would make a decision within 48 hours, but the board have given Redknapp their backing despite being relegated to the Championship.
Their fate was confirmed following their goalless draw with Reading yesterday.
Redknapp is under no illusion about the challenge facing QPR next season, but he is determined to get them promoted back to the Premier League.
He said: "Next year will be a big challenge as there are a lot of good teams and massive clubs in the Championship.
"There are big clubs who have all been in the Premier League before and we are just one of them.
Harry Redknapp shaking hands with Reading manager Nigel Adkins after both clubs were relegated
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"There is a lot of hard work to be done this summer. It's a really good challenge, it's possible, but it's not going to be easy."
Sky Bet had installed Redknapp as the next Premier League manager to lose his job, and had offered odds of 11/8.
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