Despite opposition from religious and pro-life groups, MPs in the House of Commons backed the human embryology and fertilisation bill by 355 votes to 129. It will now go to a vote in the House of Lords, and could be law by November.
The wide-ranging bill, which has been debated for months, would also allow "saviour siblings" - children created as a close genetic match for a sick brother or sister so their genetic material can help treat them.
In addition, it gives lesbians and single women easier access to in-vitro fertilisation (IVF) treatment by removing requirements for clinics to consider a child's need for a father.
Health Minister Dawn Primarolo told lawmakers the bill was about helping the one in seven couples who needed fertility assistance, and about research to deal with diseases such as Alzheimer's, which affects 350,000 Britons.
Hybrid embryos, created by inserting the nuclei of a human cell into an animal egg, can ensure a more plentiful supply of stem cells for use in research into treating conditions like Alzheimer's and Parkinson's.
"It is about research to deal with the dreadful diseases and the debilitating attacks on their health from which many in our society suffer," the minister told lawmakers.
"The bill is about combining science with an ethical framework that works on behalf of humankind."
Prime Minister Gordon Brown is a strong defendant of the measures, saying Britain owes it to future generations. His son, Fraser, has cystic fibrosis, a disease which could one day benefit from embryo research.
However, 16 MPs from his ruling Labour party, including former minister Ruth Kelly, a staunch Catholic who quit the government this month, voted against the bill and religious groups warned it was the next step on a "slippery slope".
Nadine Dorries, a member of the opposition Conservative Party, told her fellow lawmakers that loopholes in the legislation raised the possibility of scientists attempting cross-breeding between humans and animals.
"Of all the experimental possibilities debated in the course of this bill, surely none is quite so utterly repulsive as the possibility of seeking to inseminate animals with human sperm," she said.
Wednesday's debate was overshadowed by complaints from all sides that the government had blocked a discussion on reforming the abortion laws. Ministers suggested they did not think the current bill was the right time to do this.