The study, which analysed data from 522 trials involving 116,477 people, found 21 common anti-depressants were all more effective at reducing symptoms of acute depression than dummy pills.
But it also showed big differences in how effective each drug is.
The authors of the report, published in the Lancet, said it showed many more people could benefit from the drugs.
There were 64.7 million prescriptions for the drugs in England in 2016 - more than double the 31 million in 2006 - but there has been a debate about how effective they are, with some trials suggesting they are no better than placebos.
The Royal College of Psychiatrists said the study "finally puts to bed the controversy on anti-depressants".
The so-called meta-analysis, which involved unpublished data in addition to information from the 522 clinical trials involving the short-term treatment of acute depression in adults, found the medications were all more effective than placebos.
However, the study found they ranged from being a third more effective than a placebo to more than twice as effective.
Lead researcher Dr Andrea Cipriani, from the University of Oxford, told the BBC: "This study is the final answer to a long-standing controversy about whether anti-depressants work for depression.
"We found the most commonly prescribed anti-depressants work for moderate to severe depression and I think this is very good news for patients and clinicians."
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