The new treatment targets an enzyme that the virus uses to make copies of itself, introducing errors into its genetic code. That should prevent it from multiplying, so keeping virus levels low in the body and reducing the severity of the disease.
Merck said that approach should make the treatment equally effective against new variants of the virus as it evolves in the future.
The UK regulator, the MHRA, said the tablet had been authorised for use in people who have mild to moderate Covid and at least one risk factor for developing severe illness such as obesity, old age, diabetes or heart disease.
The organisation's chief executive, June Raine, described it as "another therapeutic to add to our armoury against Covid-19".
"It is the world's first approved antiviral for this disease that can be taken by mouth rather than administered intravenously," she said.
"This is important, because it means it can be administered outside of a hospital setting, before Covid-19 has progressed to a severe stage."
England's deputy chief medical officer, Prof Jonathan Van-Tam, warned on Wednesday of some "hard months to come" in the pandemic.
He said that while Covid cases appeared to have stabilised, deaths were rising and there were signs infections were starting to "penetrate" older age groups.
The UK recorded 41,242 Covid cases on Thursday and 214 deaths within 28 days of a positive test.
The results were published in a press release and have not yet been peer-reviewed.
But data suggest molnupiravir needs to be taken soon after symptoms develop to have an effect. An earlier study in patients who had already been hospitalised with severe Covid was halted after disappointing results.
In its approval document, the MHRA recommends the drug is used "as soon as possible" following a positive Covid test and within five days of symptoms onset.
Prof Penny Ward, from King's College London, who was not involved in the study, said: "If these outcomes are replicated in the UK population, then the number of cases requiring hospital admission could be halved and the number of deaths greatly reduced.
"It seems likely that it will be restricted for use by those at highest risk of disease complications - for example older adults with heart, lung or kidney disease, diabetes or cancer."
The UK government has not disclosed how much its initial contract for 480,000 courses of molnupiravir is worth. But US authorities recently made an advance purchase of 1.7 million courses at a cost of roughly $1.2 billion, or $700 (£513) for each patient.
Other countries including Australia, Singapore and South Korea have also made purchase agreements.
Merck is the first company to report trial results of a pill to treat Covid, but other companies are working on similar treatments.
Its US rival Pfizer has started trials of two different antiviral tablets, while Swiss company Roche is working on a similar medication.