Scientists have calculated that a woman's risk of breast cancer rises by 6% for each extra alcoholic drink she consumes on an average daily basis (7% on international measures).
The study, by the charity Cancer Research UK, estimates that alcohol accounts for around 4% of breast cancers in the developed world and around 2,000 cases each year in the UK alone.
And if women's alcohol consumption continues to increase this figure is likely to rise.
Previously, it has been extremely difficult for researchers to separate the effects of tobacco from the effects of alcohol because the more women drink the more they tend to smoke and vice versa.
This is a major reason why previous work has yielded conflicting results.
But the new study has overcome this problem by examining data on approximately 150,000 women from across the globe.
Over 23,000 of these women did not drink and looking at this group separately the researchers could see no significant difference between rates of breast cancer in smokers and non-smokers.
Sir Richard Doll, a co-author of the study, said: "There has been a great deal of research on whether smoking or alcohol contribute to breast cancer but until now results have been confused.
"For the first time we have undertaken a study large enough and detailed enough to look at the separate effects of tobacco and alcohol reliably.
"When we did this we found that drinking, but not smoking, increases the risk of breast cancer."
He added: "While breast cancer is the most common form of cancer in women, survival rates are relatively good.
"A woman is more likely to die of lung cancer because it is notoriously difficult to treat and lung cancer is dependent on smoking but not drinking."
Co-author Professor Valerie Beral, of Cancer Research UK's Cancer Epidemiology Unit at the Radcliffe Infirmary in Oxford, said: "This research tells us there is a definite link between alcohol and breast cancer and the evidence suggests that the more a woman drinks the greater her risk.
"The impact of drinking on breast cancer is small compared to childbearing factors, but women are drinking more now than they used to and if this pattern continues it is bound to have an impact on the rates of breast cancer in the future."
Young women drink heavily
The average alcohol intake for UK women has increased from about seven grams to eight grams per day in the last decade - but the rise has been greater among young women.
Among women aged between 16 and 24, the proportion drinking more than three drinks per day has doubled from 9% to 18%.
While women who drink are at a higher risk of a number of diseases including cancers of the throat and liver, they are at a lower risk of heart disease and stroke than non-drinkers.
Dr Gillian Reeves, who also worked on the new report, said: "The balance between the harmful effects of alcohol on breast cancer and its beneficial effects on heart disease depend on a woman's age.
"Before about 60, breast cancer is a more important cause of death than heart disease.
"After the age of 65 or so, when the risk of heart disease becomes much greater than the risk of breast cancer, the benefits of moderate drinking are more apparent."
The reason why alcohol increases the risk of breast cancer are unclear, but women with higher levels of alcohol intake tend to have higher levels of the sex hormone oestrogen in their blood.
Oestrogen is known to be linked to breast cancer.
By the age of 80 breast cancer will affect 8.8 out of every 100 women.
Among women who drink one alcoholic drink a day, the figure rises to 9.4 cases per 100.
And among those who have six drinks a day the figure is 13.3 cases per 100.
The research is published in the British Journal of Cancer.