The 67-year-old Redknapp cited impending knee replacement surgery as the reason for unexpectedly relinquishing control of a team facing relegation.
"It means I won't be able to be out on the training pitch every day," Redknapp said in a statement. "And if I can't give 100 per cent, I feel it's better for someone else to take over the reins."
The announcement came hours after the final transfer window of the season closed without the London club's squad being strengthened to cope with the final months of the season.
Redknapp, who presided over QPR's 2013 relegation and immediate return to the topflight, leaves the team 19th in the 20-team standings with 45 points still to play for.
"I know what people think — that I've been sacked, or stormed off because we couldn't get the players in," Redknapp told the Daily Mail newspaper's website. "My son Jamie said that my timing has to be the worst in the world."
Or the best for QPR's prospects of survival. QPR has lost all 11 away games. Les Ferdinand, the head of football operations, has taken temporary charge with coach Chris Ramsey while QPR seeks a new manager.
Given Redknapp's age and struggles at QPR, it would seem unlikely he would gain another Premier League job. Returning to the lower leagues — where Redknapp started his managerial career 32 years ago — might be a challenge too far for a man already beyond retirement age.
But Redknapp harbours hopes of a return to the dugout once he is fully fit.
"I still don't think I'm finished with football," Redknapp said. "When I've had the operations, I'll be looking for work again, I know that. I can't imagine my life without it."
After playing for West Ham and Bournemouth, the Londoner's coaching career in England began on the south-coast at Bournemouth.
In nine years, Redknapp unlocked the potential of an underachieving side, taking Bournemouth to the second tier of English football and famously knocking Manchester United out of the 1984 FA Cup.
After leaving in 1992, a strong seven-year stint with West Ham followed before six years at Portsmouth, interrupted by a short-lived and controversial move to local rival Southampton.
It was at Portsmouth where Redknapp's stock soared by leading the team in 2008 to its first FA Cup win in 69 years.
The triumph earned Redknapp a shot at a major job for the first time, hired later in 2008 by Tottenham when the team was bottom. He oversaw an eye-catching turnaround, steering Spurs into the Champions League for the first time in 2010 and producing memorable wins over both Inter and AC Milan.
In 2012, Redknapp looked primed to ascend to the top job in English football when he was cleared in court of tax evasion on the same day national team coach Fabio Capello quit.
But the speculation over Redknapp's future coincided with Tottenham's fortunes plummeting and the team failing to qualify for the Champions League again. In a sudden reversal of fortunes, the English FA went for the more conservative appointment of Roy Hodgson and Redknapp was fired by Tottenham.
But within months Redknapp was back in work at QPR, starting the job with strident and outspoken comments about the squad that were the media-friendly manager's hallmark.
Redknapp was tasked with performing the same rescue act that was so successful at Tottenham, but QPR was relegated in May 2013. Although QPR returned to the Premier League at the first opportunity, it only came through the playoffs and the team has struggled this season.
Failing to learn from past mistakes of signing veterans past their prime, QPR brought in Rio Ferdinand last year when he left Manchester United at 35.
And Redknapp's job prospects always seemed precarious during a season when he was not afraid to speak his mind. After claiming Adel Taarabt was overweight, the midfielder fought back in public. It prompted Redknapp to call Taarabt "the worst professional I have ever come across" before chairman Tony Fernandes expressed his disappointment with both his manager and player.
Then a month ago when reports emerged that Redknapp's job was on the line, he accused a Loftus Road insider of trying to end his reign.
"I wasn't born yesterday," he said. "Someone has said something, but it's not a problem."
Now Redknapp is stressing his departure was amicable.
Rob Harris can be followed at www.twitter.com/RobHarris