An HFEA consultation showed the public were "at ease" with the idea when told it could pave the way for therapies for conditions such as Alzheimer's disease.
Opponents have said many people would be "horrified" by such a move....
WHAT HAPPENS ELSEWHERE?
Australia - Embryos allowed to be created for research, but human-animal hybrids banned. The only exception is to test the quality of sperm
Canada - Legislation bans the creation of human-animal embryos
US - Federal funds can only be used for research involving pre-existing embryos - such as those left over from fertility treatment - and there is a ban on hybrid embryos
Elsewhere - Other countries do not specifically legislate on hybrid embryos. But Italy and Germany only allow the use of pre-existing embryos and many others including Austria, Norway and Tunisia do not allow embryo research at all
Scientists want to create hybrid embryos by merging human cells with animal eggs in a bid to extract stem cells. The embryos would then be destroyed within 14 days.
The cells form the basic building blocks of the body and have the potential to become any tissue, making them essential for research.
At the moment, scientists have to rely on human eggs left over from fertility treatment, but they are in short supply and are not always good quality.
Two teams from Kings College London and Newcastle University have already applied to the HFEA to use hybrid embryos.
It is now expected individual hearings for these two applications will be held in November with other scientists expected to follow suit.
Dr Stephen Minger, of King's College London, said he "applauded" the HFEA for its decision as it was the only ethically justifiable option if scientists were to push forward with their research.
Lyle Armstrong, of Newcastle University, added: "This is excellent news. It is a positive outcome not just for our work but for the progress of British science in general and we hope that this will lead to new technologies to benefit everyone."
And he also said: "It does seem a little abhorrent at first analysis, but you have to understand we are using very, very little information from the cow in order to do this reprogramming idea.
"It's not our intention to create any bizarre cow-human hybrid, we want to use those cells to understand how to make human stem cells better."
Our top-class researchers can now proceed with their applications to conduct this world-leading research
Dr Evan Harris
Lib Dem MP
Lib Dem MP Dr Evan Harris, a member of the Commons' science and technology committee, which has already given its backing to such research, said: "Our top-class researchers can now proceed with their applications to conduct this world-leading research."
And Dr Tony Calland, chairman of the British Medical Assocition's ethics committee, said it could lead to "major breakthroughs in treatments for Alzheimer's, Parkinson's and other serious diseases".
The HFEA decision comes amid government moves to lay down regulations covering such research - the law governing embryo research is out of date and does not cover the issue.
The government originally proposed banning the technique in a white paper last year.
But it reversed its decision this year in a bill which indicated ministers were minded to allow hybrid embryos which were 99.9% human and 0.1% animal, following a backlash by scientists and patient groups.
But the HFEA has carried out its own review ahead of parliament passing the legislation so as not to hold back research.
The regulator can grant licences to scientists to pursue such research, but will have to change its criteria if future rules contradicted its own practices.
Anthony Ozimic, secretary of pro-life group the Society for the Protection of Unborn Children (SPUC) said he "deplored" the HFEA's decision.
"This is not just a case of the 'yuk' factor - there are grave ethical and moral objections to this research and the way it is being promoted."
Using hybrid embryos has never been acceptable - it offends the dignity of humans and animals
Comment on Reproductive Ethics
And Josephine Quintavalle, of the campaign group Comment on Reproductive Ethics, said the HFEA was wrong to be pushing ahead with a decision which should be left to parliament.
"Using hybrid embryos has never been acceptable - it offends the dignity of humans and animals."
A spokeswoman for the HFEA said the decision had been a challenging one to reach.
"This is not a total green light for hybrid research, but recognition that this area of research can, with caution and careful scrutiny, be permitted."
But she added that public opinion was "very finely divided" with people only supporting it if it was tightly regulated and likely to lead to medical advancements.