Radcliffe has been struggling with a chronic foot problem and after a fitness test on Sunday it was concluded that she “would not be able to race competitively to the best of her abilities”.
The British Olympic Association intends to nominate Freya Murray as Radcliffe’s replacement.
Radcliffe said: “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.
“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.
“My sport is a beautiful sport, it gives so much fun and enjoyment, I believe 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.
“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.”
The 38-year-old added: “As desperate as I was to be part of the amazing experience of the London Olympics, I don’t want to be there below my best. If I can’t be there and give it my best, then I would rather someone else who can do that is able to be there.
“I have been through the mill emotionally and physically the past three weeks, cried more tears than ever, vented more frustration and at the same time calmly tried every direction and avenue available to heal myself.