given more information about the potential harms of being tested.
An independent review was set up to settle a fierce debate about whether the measure did more harm than good.
It showed that for every life saved, three women had treatment for a cancer which would never have been fatal.
The information will be included on leaflets to give women an "informed choice", the government said.
Cancer charities said women should still take up the offer of screening.
Screening has been a fixture in diagnosing breast cancer for more than two decades. Women aged between 50 and 70 are invited to have a mammogram every three years. It helps doctors catch cancer early so treatment can be given when it is more likely to save lives.
However, the national cancer director Prof Sir Mike Richards said it had become "an area of high controversy".
The debate centres around the concept of "over-diagnosis", that is screening which correctly identifies a tumour, but one which would never have caused harm. It leads to women who would have lived full and healthy lives having treatments - such as surgery, hormone therapy, radiotherapy and chemotherapy - which have considerable side-effects.
There is no way of knowing which tumours will be deadly and which could have been left alone.
The review, published in the Lancet medical journal, showed that screening saved 1,307 lives every year in the UK, but led to 3,971 women having unnecessary treatment. From the point of view of a single patient they have a 1% chance of being over-diagnosed if they go for screening.
The independent review panel was led by Prof Michael Marmot, from University College London. He said screening had "contributed to reducing deaths" but also "resulted in some overdiagnosis".
He said it was "vital" women were told about the potential harms and benefits before going for a mammogram.
Cancer charities have unanimously argued that women should still choose to be screened
Prof Richards said: "My view is that the screening programme should happen, we should invite women to be screened and give women the information to make their own choice."
He said the leaflets on breast cancer screening sent to women would be updated in the "next few months" to "give the facts in a clear, unbiased way".
Current advice does not highlight the scale of the risk.