Britain last year became the first country in the world to legally offer such a treatment after parliament approved legislation in December.
Doctors at the Newcastle Fertility Centre in northeast England will however not be able to go ahead with technique until an application by an individual patient has been approved.
"This significant decision represents the culmination of many years hard work by researchers, clinical experts and regulators," said Sally Cheshire, head of the Human Fertilisation and Embryology Authority.
British lawmakers voted in 2016 to allow the treatment, in which the DNA of the mother, father and a female donor are combined to create a baby.
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Mitochondria are structures in cells which generate vital energy and contain their own set of genes called mDNA which is passed through the mother.
Mitochondrial diseases cause symptoms ranging from poor vision to diabetes and muscle wasting, and health officials estimate around 125 babies are born with the mutations in Britain every year.
Around 3,000 British families could benefit from the therapy, but Cheshire said she expected that "many won't come forward".
The treatment remains controversial in Britain and elsewhere, with religious leaders among its detractors.
The Roman Catholic Church opposes the move, pointing out that it would involve the destruction of human embryos as part of the process, while the Church of England has said ethical concerns "have not been sufficiently explored".