The Government's chief medical officer, Professor Dame Sally Davies, has said she is "delighted" that MPs passed the amendment and that she hopes the Lords will do the same.
She said: "Mitochondrial donation 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," Dame Sally added.
MPs have voted in favour of a ground-breaking but controversial technique that could see IVF babies conceived with DNA from three people.
A vote on three-parent babies, taking place today, could determine paediatric nurse Rachel Steel's chances of having her own healthy kids.
The parents of a baby with a life-limiting disorder say their future happiness will be decided by today's three-parent family vote.