Newcastle University researchers will be allowed to create embryos which could be used to treat conditions such as diabetes and Alzheimer's disease.
The embryos will be destroyed before they are 14 days old. There's no chance of them being used to make a baby.
But scientists say it will be at least five years before patients could benefit from their research.
Cloning to create copies of human babies is illegal in Britain, but it's OK to clone embryos for medical purposes.
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It's thought the research might be able to help millions of people in the future.
Human embryos have already been cloned in some places, but this is thought to be the first time it's been allowed to happen in Europe.