QPR chairman Tony Fernandes said: "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."
Fernandes continued: "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."
A announcement regarding Redknapp's backroom team will be made in due course.
More top news
Dry with sunny spells to start. Warm with hazy sunshine this afternoon
A dry and bright start with long spells of sunshine into this afternoon and feeling fresher
Fine this evening, then dry overnight with mist likely in places. Sunny spells tomorrow morning with hazy sunshine in the afternoon