The baby, Abrahim Hassan, was born five months ago.
His mother carries genes for Leigh syndrome, a rare genetic disorder that causes the degeneration of the central nervous system and vital organs.
The couple had been trying to start a family for 20 years, but their first two children each died as a result of the condition, leading them to seek out the controversial technique.
Doctors at the New Hope Fertility Centre in New York removed the nucleus from one of the mother's eggs and inserted it into a donor egg, then used during fertilisation.
The embryo was implanted in the baby's mother, and, nine months later, Abrahim Hassan was born.
However, the baby carries only one-hundredth of 1 per cent of the donor's DNA.
Dr John Zhang, who conducted the advanced form of IVF, explained the procedure to the BBC.
"In this way, we can reduce the defective structure in her egg so she can have a healthy baby but still using her own DNA, but borrow the material from the donor."
Oxford University's Dr Dagan Wells tested the embryos before they were implanted in the mother.
He says he is encouraged.
"I'm very excited by this. I think it's something that so many scientists have been working towards for such a long time, and to see it finally coming to fruition is enormously encouraging."
The controversial technique is illegal globally and has only been legally approved in Britain.
That is because it carries both health risks and ethical complications.
However, a US medical team carried out the birth, treating Ibtisam Shaban and her husband Mahmoud Hassan in Mexico, where there are no laws against the procedure.
A senior lecturer in stem-cell science at Kings College in London, Dr Dusko Illic, has told the BBC the breakthrough is remarkable.
But he says he has concerns about how the procedure was carried out.
"It is actually giving the signal that you can do whatever you want and expose patients to risks if you go to a country that has no legislation."
In Australia, Murdoch Children's Research Institute professor David Thorburn has told the ABC the child must be monitored for years before the procedure can be deemed safe.
"There's been evidence from doing this procedure in monkeys, in macaques, that's very reassuring. There are theoretical concerns that can't really be answered completely until these sort of children have been monitored for a significant period of time. I think the head of the Wellcome Trust in the UK said this was probably the most rigorously investigated scientific endeavour that will ever be introduced into humans, so the amount of work that's gone into it is very high, considering the safety issues. But with any medical advance, there's always some residual concern."
