In the House of Commons, 382 MPs were in favour and 128 against the technique that stops genetic diseases being passed from mother to child.
During the historic debate, ministers said the technique was "light at the end of a dark tunnel" for families.
Proponents said the backing was "good news for progressive medicine".
A further vote is required in the House of Lords for complete clearance. If everything goes ahead, then the first such baby could be born next year.
The British Parliament was to decide whether to allow the creation of IVF babies using DNA from three people – mother, father and a female donor.
The technique is aimed at preventing deadly genetic diseases being passed from mother to child and is expected to help about 150 couples a year.
However, the move has sparked a fierce ethical debate with senior Church figures calling for the procedure to be blocked.
The UK government backed the measure in principle but all MPs were given a free vote rather than being forced down party ines as it is an issue of conscience.
They voted on mitochondrial DNA (mDNA) donation techniques aimed at preventing serious inherited diseases.
mDNA is passed on through the mother and hereditary mitochondrial diseases affect major organs and cause symptoms ranging from poor vision to diabetes and muscle wasting.
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.

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