A rescue team found the men yesterday after the son of one of the mountaineers trekked down through the snowstorm and reported the group's whereabouts.
Colin Riddihough, 46, Paul Dick, 56, and John Plews, 30, froze to death after being caught in the severe snowstorm over the weekend. The mountain range in Andalucia has some of the highest passes and most hostile conditions in Europe.
Two Spanish hikers, who were climbing the north side of Mulhacén, turned up safely yesterday after failing to return home on Sunday night. They too had been stranded by the snowstorm.
Last night, neighbours of the British men, from Brotton, on Teesside, said they were pursuing the sport they loved. One said: "They were all very keen mountaineers, they loved the outdoors. They were all fit guys and would do peak challenges in the Lake District.
"It is a dreadful thing to have happened. Three local families are devastated and the whole village is thinking about them and praying for them."
The Britons began their hike on Sunday wearing inadequate clothing and footwear, despite warnings that bad weather was expected. One police spokesman described their expedition as "reckless".
They apparently got lost on the southern face of Mulhacén, the highest mountain in mainland Spain, which rises above the city of Granada. They tried to take shelter in a refuge they dug in the snow, while Mr Riddihough's son Steve, 30, left to find help.
He reached the town of Capileira on Sunday afternoon where he alerted the police mountain rescue service. A search operation was mounted immediately and worked until nightfall. Rescue efforts were reinforced at dawn yesterday with the aid of a helicopter.
The men were found in the afternoon in Collado de Mulhacén, and were transferred by helicopter to Capileira, in the Alpujarras region, for autopsy.
Mr Riddihough had been in the Army and was working in a potash mine at Boulby, North Yorkshire, when he left for the climb with his son. He was married and also had a daughter.
He and Mr Dick went hill climbing in the Lake District every other weekend. Mr Riddihough used to organise the trips and the group's minibus.
Mr Dick, his neighbour, was separated from his wife and had a sonand daughter, both in their 20s. He had worked in Saudi Arabia for some years and until recently was working at a Tesco's in Redcar, Teesside.
A Foreign Office spokesman said yesterday: "The weather conditions became so treacherous that they made a shelter for the night. It seems one of them made it down and alerted the search and rescue teams." He confirmed that the three mountaineers died of hypothermia.
The Sierra Nevada range has more than 20 summits above 10,000ft. Mulhacén, at 11,414ft (3,479m), is more than two-and-a-half times higher than Britain's highest mountain, Ben Nevis.
Temperatures on the peaks are on average 14C less than in the surrounding valleys, making sub-zero conditions a constant occurrence during the colder months of the year. Conditions are brutal when severe snowstorms hit. In May 2004, rescuers found the bodies of three people, including two Dutch women, who were in a group of climbers who got lost in bad weather.
Last month, Paul Beck, 33, from London, was rescued after spending five days in sub-zero temperatures in northern Spain. He survived by drinking his own urine and eating oats, dry rice and powdered chocolate while stranded in the Picos de Europa in Asturias. A fortnight ago, a British couple also froze to death in the Picos after they were engulfed by a whiteout and lost their bearings.
The body of a Spanish skiier who went missing on Sunday was found buried in an avalanche near Lerida, in Catalonia, yesterday.
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