There had been prolonged speculation the 38-year-old world record holder, who has never won an Olympic medal of any colour, would pull out because of her foot problem and Radcliffe confirmed her exit in a statement on Sunday.
“From the day when it was announced that London had won the bid, taking part and performing well in the London Olympic Games has been a major goal in my life,” Radcliffe said.
“The goal of a fifth Olympics in my home country, what better? The chance to make amends to myself for bitter disappointments at the previous two Olympics.
“Through a lot of tough times it has kept me fighting, motivated and focused. That is why it hurts so much to finally admit to myself that it isn’t going to happen,” added Radcliffe, who will be 42 by the time of the 2016 Games in Rio.
Radcliffe, whose career has been blighted by injury and illness, tried to put a brave face on her crushing disappointment.
“My sport is a beautiful sport, it gives so much fun and enjoyment, I believe it helps me to be a better person, and I have been very fortunate to experience some great success and have so many beautiful and happy memories,” she insisted.
“However, the downside is that it can break your heart and spirit many times over when your body is simply unable to match what your heart and brain want it to do.
“Sadly mine is not a career or a hobby where mind over matter can work when your body is hurt, nor where giving less than your best each day can ever work.”
UK Athletics head coach Charles van Commenee added: “This is obviously a disappointing day for Paula and our sport, but it was important to her that if she made the start line it would be in the best possible shape.
“It wasn’t meant to be and she has taken the right decision to withdraw at this stage,” the Dutchman added.
“I think it is important that we don’t look at Paula’s career in Olympic cycles. She is undoubtedly one of the greatest female distance runners of all times and still holds the marathon world record.
“I wish her all the very best for her recovery.”
Radcliffe has run some of the fastest marathons in history but Olympic glory has always proved elusive.
At the 2004 Athens Games, she was forced to stop mid-race and dissolved into tears.
Radcliffe was hampered by injury again four years ago in Beijing when she trailed home in the marathon in 23rd place after a stress fracture had disrupted her training.