Kenton Cool, 38, from Gloucestershire, reached the summit at midnight UK time.
It breaks his own British record for the most summits of Everest - he has now scaled the world's highest peak 10 times.
Mr Cool carried a medal from the 1924 Winter Olympics, fulfilling a pledge made by a member of the 1922 British Everest expedition.
His team said he spent about 30 minutes at the top before beginning his descent.
"To stand on the summit for the 10th time is simply amazing," Mr Cool said in a message sent via his expedition team.
"To have with me an Olympic Gold medal awarded to the 1922 team is humbling.
"This promise needed keeping, and after 90 years the pledge has been honoured for Britain."
The British Everest expedition in 1922 came within 500m of the summit, but failed three times to reach the top.
At the 1924 Winter Olympics in Chamonix, France, 21 team members were honoured with medals for mountaineering.
Lt Col Edward Strutt, who was the expedition's deputy leader, pledged to place one of the medals on the summit of Everest, but the promise was never kept.
Speaking to the BBC from Camp 3 on his way down, Mr Cool said: "When we got the medal out at the top I pretty much broke down in tears.
"At the summit we took it out and did some filming, took some photographs and I made a few silent prayers."
Mr Cool added that he had left the medal alone for a few minutes at the top because "it deserved some time there on its own".
"As soon as we'd finished the winds were really vicious so it was straight back down to safety."
Rhys Jones, who became the youngest person to climb Everest in 2006, congratulated Mr Cool on his feat.
"Kenton is in a league of his own," he said.
"It takes so much guts and endurance to put your body through that once - not just the climb itself, but the months of preparation and training - to do it 10 times is a truly fantastic achievement."
Mr Cool was loaned one of the medals awarded to the team from 1922 by Charles Wakefield, the grandson of Dr Arthur Wakefield who was a member of the expedition.
Mr Cool has also been chosen to be an Olympic torchbearer in the run-up to the London 2012 Olympic Games and is due to be back in the UK in time to take part in July.
A British climber has successfully carried an Olympic gold medal to the top of Mount Everest.