Harry Taylor's fellow expedition members, John Barry and Rebecca Stephens - who had hoped to be the first British woman to scale the peak - abandoned their attempt to help care for him.
Mr Taylor, 33, had been three nights at high altitudes without oxygen. His solo climb lasted about 24 hours.
The veteran climber walked to his colleagues' tent at Camp 4 on Sunday evening, just as expedition organisers were expressing concern for his safety. He was several hours overdue in worsening weather and had been out of radio contact for some time.
Organisers of the D H L Everest 40 expedition said Mr Taylor was the first man to scale Everest from the Nepalese side without oxygen and had almost certainly set a record for endurance without oxygen at such altitudes.
After 48 hours in such conditions brain damage becomes a serious risk. An expedition spokesman said Mr Taylor had so far spoken little of his ordeal other than to confirm he made the summit. 'He is absolutely exhausted and in quite a bad way,' the spokesman said, adding that the temperature was minus 35 C.
Mr Taylor, one of Britain's top mountaineers, had climbed the world's highest peak on four previous occasions.
In 1988, he tackled one of Everest's last unconquered routes, the treacherous north- east ridge, with Russell Brice, a New Zealander.
A 50-year-old Merseyside man set a world record after crossing the Atlantic Ocean in a boat the size of a bath tub. Tom McNally, a painter and arts teacher from Liverpool, arrived in Puerto Rico yesterday lunchtime aboard the 5ft 41 2 in long Vera Hugh, Pride of Merseyside, after a three-month voyage. It is the smallest vessel to have successfully navigated any of the world's oceans.