His efforts this time are raising money for the Marie Curie Cancer Care charity - his wife, mother and sister all died from the disease within 18 months.
The BBC's Andrew North joined Sir Ranulph during the first two days of the climb and said it was obvious that a "bull-headed determination" drove him on.
EVEREST FACTS AND FIGURES
Height: 8,848 - 8,850m (29,029 - 29,035 feet)
First ascent: 29 May, 1953, Edmund Hillary/Tenzing Norgay
Number of ascents up to 1988: less than 200
Number of ascents up to end of 2008 climbing season: 4,109 by 2,700 individuals
Most people on the summit in a single day: 116, on 22 May, 2003
Oldest summiteer: 76-year-old Nepalese man, Min Bahadur Sherchan
The adventurer spoke to our correspondent by radio from the summit.
"He did say he was really pleased to have got there. He also said he felt dreadful, exhausted from the climb and was looking forward to getting down," said Mr North.
"You could tell he was very relieved," he said, adding that the pace of his climb was "remarkably fast" having reached the summit from the highest camp in just nine hours.
During his career Sir Ranulph has led more than 30 expeditions.
The explorer is perhaps best known for a three-year transglobe expedition - the first successful circumnavigation of the world on its polar axis - which was completed in 1982.
He also travelled to the North Pole unaided, along with Dr Mike Stroud, as well as a 97-day trek across Antarctica.
Sir Ranulph had a triple heart bypass in 2003 after suffering from a heart attack.
Only four months later, he and Dr Stroud ran seven marathons in seven days on seven continents.
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