The medicine is specifically for the recurring form of malaria, 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.
Recurring malaria – caused by the parasite plasmodium vivax – is the most common type of malaria outside sub-Saharan Africa.
Children can be particularly at risk, getting several bouts of malaria from a single bite, missing lots of school and getting weaker each time they get the disease.
And infected people can act as unwitting reservoirs of the disease because when the parasite reawakens in their bodies a mosquito can carry that parasite on to someone else.
This can make it hard to eliminate around the world.
Now the Food and Drug Administration (FDA) in the United States of America has given the seal of approval to tafenoquine, a drug that can flush the parasite out of its hiding place in the liver and stop people getting it again.
It can be taken alongside another medicine to treat the immediate infection.
There is already a medication that can be used to get rid of malaria hiding in the liver called primaquine.
But unlike the single dose of tafenoquine needed, primaquine often needs to be taken for 14 days.
Some experts are concerned that many people feel better after just a few days and stop taking the pills, allowing the parasite to awaken at a later date.
The FDA says the drug is effective and approves it for use in the United States of America but points out that there are important side effects to be aware of.
For example, people with an enzyme problem, called G6PD deficiency, should not take the drug as it can cause severe anaemia.
The regulator recommends people are tested for the deficiency for this before it is given – which can pose a problem in poorer areas where malaria is common.
There are also concerns that at higher doses it can be a problem for people with psychiatric illnesses.
But despite these cautions, there is hope the drug, together with bed nets and other precautions, will help reduce the amount of vivax malaria in the world.