In a free vote, the Commons vote 382 for and 127 against.
The UK is one step closer to becoming the first country to carry this out.
The issue now goes to the House of Lords and if it passes there it could lead to the first such baby being born next year.
It comes after a new poll by Christian charity CARE showed just 10% of the public was in favour of the proposals.
The mitochondrial donation is aimed at stopping serious inherited diseases that can be devastating to a person's life and cause early death.
Research suggests the technique could help almost 2,500 women in the UK have children.
But the Catholic Church said it had "serious ethical objections" to the proposals.
The Church of England has also criticised the coalition's plan.
The research by CARE, carried out by ComRes, showed the majority of the public thought the government should wait for the conclusion of all the pre-clinical safety tests that the Human Fertilisation and Embryology Authority advised the Government should take place before proceeding.
CARE's Director of Parliamentary Affairs Dr Dan Boucher said: "From the outset we have been arguing that the regulations should not be put to the Parliament until all of the advised pre-clinical safety tests have been concluded.
"The Department of Health has not listened and these figures clearly reveal the majority of people think they are wrong to try to push the regulations through without waiting for the conclusion of the pre-clinical safety tests.
"The figures also show that, setting the questions of the safety tests to one side, more than twice as many people are against the proposals than are in favour.
"Not for one minute would we deny that mitochondrial diseases are terrible to deal with.
"But MPs must consider the dangers of rushing these regulations through when we simply do not know the true consequences of doing so.
"The reality is we don't know all there is to know about how this technique will affect the child and females created using this new technique would have to be monitored, as the HFEA has recommended, for the rest of their lives as such any of their children."
"More and more evidence also seems to indicate mitochondrial DNA informs the characteristics of the child and because of this CARE is firmly of the view that the term "three parent children" is entirely accurate."
Dr Jeremy Farrar, director of the Wellcome Trust, the UK's biggest research charity, said: "Over the past seven years, Britain has been engaged in an exemplary process for evaluating scientific, ethical and public opinion about mitochondrial donation, which has revealed broad support on all three fronts.
"The Government is right to ask Parliament to support regulations that will allow the law to catch up with public and scientific opinion, and we urge MPs and peers to vote for them."
You can listen to interviews with James Mildred from CARE and Paul Preston from The Children's Mitochondrial Disease Network, who both appeared on Premier's News Hour.
