Scientists also discovered that cholesterol-lowering statin drugs can reduce its harmful effects.
Previous studies had already shown a link between raised cholesterol and breast cancer, but one that could not be explained.
The new US research, conducted on mice, shows for the first time how a breakdown product of cholesterol called 27HC drives breast cancer by mimicking the effects of the hormone oestrogen.
Three quarters of breast cancers are sensitive to oestrogen, which stimulates tumour growth.
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Lead scientist Dr Donald McDonnell, from Duke University Medical Center in Durham, North Carolina, said:
"A lot of studies have shown a connection between obesity and breast cancer, and specifically that elevated cholesterol is associated with breast cancer risk, but no mechanism has been identified.
"What we have now found is a molecule - not cholesterol itself, but an abundant metabolite of cholesterol - called 27HC that mimics the hormone oestrogen and can independently drive the growth of breast cancer."
Earlier research from Dr McDonnell's laboratory confirmed that 27HC - full name 27-hydroxycholesterol - behaves like oestrogen in animals.
The latest study, published in the journal Science, found that daily injections of 27HC caused the tumours of mice with breast cancer to grow and spread more rapidly.
Further work on laboratory samples of human cancer cells showed the most aggressive produced higher levels of an enzyme that generates 27HC from cholesterol.
"The worse the tumours, the more they have of the enzyme," said co-author Dr Erik Nelson, also from Duke University.
Feeding mice the statin drug atorvastatin both reduced their circulating cholesterol levels and tumour growth.
The research also revealed a potential link between 27HC and the development of resistance to the widely-used breast drug tamoxifen, which blocks the cancer-fuelling effects of oestrogen.
"This is a very significant finding," said Dr McDonnell.
"Human breast tumours, because they express this enzyme to make 27HC, are making an oestrogen-like molecule that can promote the growth of the tumour. In essence, the tumours have developed a mechanism to use a different source of fuel."
As well as reducing cancer risk, keeping cholesterol in check with a healthy diet or by taking statins may delay resistance to hormonal breast cancer therapies, he added.
Clinical trials are now needed to investigate whether breast cancer really can be tackled by targeting cholesterol, said the scientists, who suggested that 27HC may also play a role in other cancers.