The breakthrough by UK researchers opens up the possibility of families blighted by serious illnesses being able to avoid these problems in their children.
The technique would involve swapping the genetic material from parents affected by these diseases to healthy, donated eggs.
This would mean a child could be produced using the parents' DNA, via an egg donated by another woman.
Experts hailed the advance – the first time it has been successfully used in human eggs after previous research in monkeys.
The technique, outlined in the journal Nature, opens up the prospect of families avoiding mitochondrial disorders, which are passed on through the mother's genes. Around one in 6,500 children in the UK is severely affected by the disorders, which can cause muscle weakness, blindness, heart and liver failure, diabetes and learning disabilities.
The new technique, developed at the University of Newcastle, raises the hope of ensuring a baby does not inherit malfunctioning mitochondrial DNA. The fertilised egg from the parents usually contains two pronuclei – genetic material from the egg and sperm – plus the defective mitochondria.
A fertilised egg from a donor, without mitochondrial defects, has its own pronuclei removed – essentially removing the donor's DNA. The parents' pronuclei are then put inside the donor egg.
The new fertilised egg then contains the DNA of the mother and father, but the healthy mitochondria from the donor.
"What we've done is like changing the battery on a laptop," said Professor Doug Turnbull, one of the study leaders. "The energy supply now works properly, but none of the information on the hard drive has been changed.
"A child would have correctly functioning mitochondria, but in every other respect would get all their genetic information from their father and mother."
Prof Alison Murdoch, who was also involved in the study, said it would be quite wrong to talk of such children having "two mothers" as
mitochondrial DNA had none of the "parental" effects of nuclear DNA, with no impact on a child's appearance or make-up.
Prof Turnbull said there was no technical reason the technique should not be available within three years. There were legal and ethical challenges ahead, though. Under the Human Fertilisation and Embryology Act it is illegal to create babies using embryos manipulated in a laboratory. But it could be done if secondary legislation allowing carefully vetted procedures is brought into force.
Negotiations with the Human Fertilisation and Embryology Authority have begun and an application made to extend research.
Dr Calum MacKellar, of the Scottish Council on Human Bioethics, said: "You cannot just reduce a parent to the DNA provider since the definition of a biological parent is a person who participated in creating the life of a child. In this case there are actually three biological parents who would all have special bonds with the prospective child."
'It would be amazing if this could be prevented'
SHARON Bernardi has a form of mitochondrial disease she inherited from her mother.
The condition has claimed the lives of six of her children, all of them dying within a few hours of being born.
Her only living son, Edward, 20, has a condition called Leigh's disease and needs constant care. He is wheelchair-bound and has to be fed liquids. His life expectancy is dramatically reduced. Ms Bernardi, 44, from Sunderland, said: "I wasn't diagnosed until after my fifth baby had died. No-one knew why it was happening..
"My mum told me it had happened to her. The previous generation lost 11 children.
"It is a devastating thing to happen, but I feel lucky to have Edward. It would be an amazing thing if scientists and doctors can prevent this in the future."