MPs have paved the way for so-called 'three-parent babies' after an historic free vote in the House of Commons today.
They voted overwhelmingly in favour of reforming the 2008 Human Fertilisation and Embryology Act by 382 votes to 128.
If the House of Lords ratifies the decision, the UK will become the first country to allow mitochondrial donation.
This controversial technique involves conceiving IVF babies with DNA from three different people to avoid devastating inherited diseases.
Pro-life groups and some Church leaders opposed the change on ethical and safety grounds.
But the Prime Minister, speaking shortly before the vote, insisted there was no question of "playing God".
David Cameron said: "As someone who had a severely disabled child himself, I know what parents go through when they are concerned about these issues.
"If science can help in this way, and I think all the arguments are in favour, we should make sure these new treatments are available."
Labour leader Ed Miliband and Deputy Prime Minister Nick Clegg also exercised their free vote to support the decision.
Under the new technique, IVF babies would still inherit the vast majority of their DNA - which determines individual traits such as facial features and personality - from their two parents.
A tiny amount of mitochondrial DNA would be donated from an anonymous woman donor.
Mitochondrial DNA makes up just 0.1% of a person's genetic code, but faults can lead to a wide range of devastating and sometimes life-threatening inherited diseases.
It can be responsible for conditions including blindness, deafness, muscle wasting, diabetes, heart failure and dementia.
Scientists led by Professor Doug Turnbull at the Wellcome Trust Centre for Mitochondrial Research at Newcastle University have pioneered the technique and hope to be the first to offer the treatment.
They believe it could potentially help almost 2,500 women of reproductive age in the UK, although they are realistically looking at "tens of families" that could be eligible.
A spokeswoman for the Wellcome Trust said if all goes according to plan the first licence will be applied for in November this year and the first baby born in 2016.
Scientists and charity leaders welcomed the decision, with the chief medical officer Professor Dame Sally Davies saying it will "give women who carry severe mitochondrial disease the opportunity to have children without passing on devastating genetic disorders.
"It will also keep the UK at the forefront of scientific development in this area," she added.
Josephine Quintavalle, from the pro-life group Comment on Reproductive Ethics, said it was a "sad, sad day for both science and ethics".
She condemned the "dangerous and unethical re-writing of human biology, no matter how virtuous the end objective of creating children without mitochondrial disease."
The Roman Catholic Church in England and Wales reiterated its staunch opposition to the procedure, chiefly because it involved sacrificing the potential "person" embodied in the donor's genetic material.
The Church of England has said it is not opposed to the treatments in principle, but has concerns about safety and the speed of progress.