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
Streets around a Dorset cul-de-sac have been cordoned off by police investigating the shooting dead of a householder by armed intruders.
Police are investigating a fatal shooting at a house in Ringwood after intruders were reported breaking into a house
Former PM David Cameron has a family fight on his hands - over who will get to use the new luxury Shepherd's Hut at his Oxfordshire home