The veteran boss says he is quitting his post because he will undergo knee replacement surgery in the coming weeks.
The 67-year-old took charge at Loftus Road in November 2012 but informed Chairman Tony Fernandes that he was resigning on Tuesday morning.
And QPR have announced that Les Ferdinand and Chris Ramsey have been placed in temporary charge of the team until further notice.
Redknapp has been under pressure this season and leaves with QPR second-bottom of the Premier League, having not earned a single point away from home all season.
QPR were expected to try and strengthen their squad while the transfer window was open but their only signing was Mauro Zarate from West Ham, who has been on the field for just 14 minutes since his arrival on loan at the start of January.
Redknapp said: “I have had such a fantastic time at QPR.
“I would like to thank the Board, the players and all my staff, and especially the supporters, who have been absolutely fantastic to me since I arrived at the club for their tremendous support.
“Sadly, I need immediate surgery on my knee, which is going to stop me from doing my job in the coming weeks.
“It means I won’t be able to be out on the training pitch every day and, if I can’t give 100 per cent, I feel it’s better for someone else to take over the reins.
“My relationship with Tony Fernandes has been one of the highlights of my footballing career and I wish the club every success. I am confident they will survive in the Premier League this year.”
Fernandes said: “I would like to take this opportunity to thank Harry for everything he has done for QPR during his time in charge.
“We part on good terms and I would personally like to wish him all the best for the future.”
Sources reveal that Harry has stressed that Queens Park Rangers’ lack of dealings in the transfer window has absolutely nothing to do with this decision.
“He insists his problems are his knees. He had a knee operation not too long ago and he tells me he has been in huge discomfort since that operation.
“He stresses that, once he gets surgery done, on one or both knees, he is coming back. In Harry’s words, ‘there is no way I am giving up football'”.
Redknapp took charge at Loftus Road following the sacking of Mark Hughes with QPR in trouble towards the bottom of the Premier League and he was unable to prevent their relegation that season.
However, QPR bounced back last term via the play-offs, securing a return to the Premier League when Bobby Zamora scored a dramatic late winning goal against Derby at Wembley.
Their home form since their return to the top flight has been reasonable but their dismal efforts away from home have consigned them to another relegation struggle, with 11 losses from 11 matches, six goals scored and 27 conceded.
The 48-year-old Ferdinand, a popular figure with the QPR fans due to his goalscoring exploits as a player for the club, was named Head of Football Operations at Loftus Road in in October and will now take temporary charge alongside Chris Ramsey.
Ferdinand and Ramsey worked as coaches under Tim Sherwood when he was in charge at Tottenham.