The drug, which California-based Gilead Sciences Inc is calling Veklury, cut the time to recovery by five days, from 15 days to 10 on average, in a large study led by the US National Institutes of Health.
It had been authorised for use on an emergency basis since spring, and now has become the first drug to win full US approval for treating Covid-19.
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Gilead says Veklury is approved for people at least 12-years-old and weighing at least 40kgs who need hospital admission for their coronavirus infection.
It works by inhibiting a substance the virus uses to make copies of itself.