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.
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Councillors in Bournemouth are due to approve an increase in council tax of almost 5% for the next financial year.
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