Donor hearts are usually from people who are brain-stem dead, but whose hearts are still beating.
In this case, the organ came from a donor after their heart and lungs had stopped functioning, so-called circulatory death.
Papworth Hospital in Cambridge said the technique could increase the number of hearts available by at least 25 per cent.
The recipient Huseyin Ulucan, 60, from London, had a heart attack in 2008.
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"Now I'm feeling stronger every day, and I walked into the hospital this morning without any problem," he said.
Non-beating-heart donors provide kidneys, livers and other organs, but until now it has not been possible to use the heart because of concerns it would suffer damage.
The new procedure involved re-starting the heart in the donor five minutes after death and perfusing it and other vital organs with blood and nutrients at body temperature.
"We had the heart beating for about 50 minutes, and by monitoring its function were able to tell that it was in very good condition," the lead transplant surgeon Stephen Large was quoted as saying by the BBC.
The organ care system is also used for maintaining lung, liver and kidneys outside the body.
The standard method for transporting hearts and other organs for transplant is to pack them in ice, but some organs can be damaged by this process.
The Papworth team said that restoring the heartbeat after death and keeping the organ nourished had helped reduce damage in the heart muscle.
There have been 171 heart transplant in the past 12 months in the UK. But demand exceeds supply, and some patients have to wait up to three years for a suitable organ. Many patients die before an organ becomes available.
TransMedics, the US company that makes the organ care machine, said each unit cost 150,000 pounds plus 25,000 pounds per patient transplanted.