The baby boy was born five months ago in Mexico to Jordanian parents, and is healthy and doing well, said the report in New Scientist magazine, described as an "exclusive."
The boy's mother carried genes for a disorder known as Leigh Syndrome, a fatal nervous system disorder which she had passed on to her two previous children who both died of the disease.
She had also suffered four miscarriages.
The woman, whose identity was withheld by New Scientist, and her husband sought the help of John Zhang, a doctor from the New Hope Fertility Center in New York City to have a baby that would be genetically related to them but would not carry the inherited disease.
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One method that has been approved in the United Kingdom, called pronuclear transfer, was deemed unacceptable to the couple because it would involve the destruction of two embryos, said the report.
Since the mother carried the genes for the disease in her mitochondria, or DNA that is passed down from the maternal side, Zhang used her nuclear DNA and combined it with mitochondria from an egg donor, in a technique known as spindle nuclear transfer.
"The resulting egg - with nuclear DNA from the mother and mitochondrial DNA from a donor - was then fertilized with the father's sperm."
Zhang and his team are expected to describe their method at the American Society for Reproductive Medicine meeting in Salt Lake City, Utah, next month.
An abstract describing the research has been published in the journal Fertility and Sterility, but outside experts said much more remains to be understood about the research.
Attempts began in the 1990s to create a baby by injecting mitochondrial DNA from a donor into the mother's egg, and adding sperm from her partner.