The medicine is specifically for the recurring form of malaria - caused by the parasite plasmodium vivax - which makes 8.5 million people ill each year.
This type of malaria is a particular challenge to get rid of as it can remain dormant in the liver for years before reawakening many times.
Scientists have described tafenoquine as a "phenomenal achievement."
Regulators around the world will now look at the drug to see if they can recommend it for their populations.
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