In a historic debate, the House of Commons voted by 382 to 128. During the debate, ministers said the technique was "light at the end of a dark tunnel" for families.
They approved the regulation in spite of some critics warning it was a step towards creating "three-parent" designer babies. The regulations will now have to be approved in the House of Lords, where they are likely to be passed.
The technique could prevent mitochondrial diseases but also raises significant ethical issues.
Passage of the law is opposed by Catholic and Anglican church leaders, in part because the process involves the destruction of an embryo.
The technique aimed at preventing deadly genetic diseases being passed from mother to child is expected to help about 150 couples a year.
One in 6,500 babies in the UK are thought to develop a serious mitochondrial disorder, which can lead to health issues such as heart and liver disease, respiratory problems, blindness and muscular dystrophy.
But the cutting-edge IVF technique involves transferring nuclear genetic material from a mother's egg or embryo into a donor egg or embryo that's had its nuclear DNA removed.
The new embryo will contain nuclear DNA from the intended father and mother, as well as healthy mitochondrial DNA from the donor embryo -- effectively creating a "three-parent" baby.
Under the proposed change to the laws on in-vitro fertilisation (IVF), as well as receiving normal "nuclear" DNA from its mother and father, the embryo would also include a small amount of healthy mDNA from a woman donor.
