The Barclays Premier League's bottom side have moved fast to replace Hughes, who was only dismissed yesterday morning.
"When I spoke to the shareholders and they told me about their plans I knew this was too good an opportunity to turn down.
"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."
Redknapp, who left Tottenham at the end of last season, takes over a side four points adrift at the foot of the table and without a win from their first 12 league games.
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.
"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."