Christopher Kulish, a lawyer from Colorado, died on Monday at a camp below the summit during his descent, and the cause of his death is unknown, Sky News reported.
The 62-year-old had just achieved his life goal of reaching the top of Everest with a small group after crowds of hundreds of climbers congested the 8,850m (29,035ft) peak last week.
In a statement, Kulish's brother Mark said, "He saw his last sunrise from the highest peak on Earth. At that instant, he became a member of the '7 Summit Club,' having scaled the highest peak on each continent."
Describing his brother as an "inveterate climber of peaks in Colorado, the West and the world over", he added, "We are heartbroken at this news."
Kulish died at the next camp below the summit on the southeast ridge after scaling Everest in nearly ideal weather, his brother said.
"He passed away doing what he loved, after returning to the next camp below the peak," he added.
His death marks the 11th fatality on Everest in recent weeks after a record 381 permits were issued to climb the mountain located in the Mahalangur Himal subrange of the Himalayas.
About half a dozen climbers died on Everest last week.
Robin Haynes Fisher died 150m (almost 500ft) below the summit as he made his way back down.
Another American climber, 55-year-old Don Cash of Utah, died after fulfilling his dream of climbing the highest mountains on each continent.
Kevin Hynes, a 56-year-old from Ireland, died in his tent in the early hours of Friday at a height of 7,000m (22,965ft) after deciding to turn back before reaching the summit.
The father-of-two had texted friends the day before to say the expedition was "proving the most fun he had had".
Another Irishman, Seamus Lawless, fell as he was descending from the peak — and a search operation to find him was called off due to adverse weather.
Most of those who have died are believed to have suffered from altitude sickness, which is caused by low amounts of oxygen at high elevation and can cause headaches, vomiting, shortness of breath and mental confusion.
Recent deaths have been exacerbated due to a crowded route to and from the summit, leading to delays. The short climbing season ends this month.
About 5,000 people have scaled the Everest Summit so far and a total of 300 have died on its slopes.
Rizza Alee, an 18-year-old climber from India's Kashmir, said that the ‘massive traffic jams’ up the mountain had made scaling Everest a ‘death race’.
He said he was distraught after he had to abort his climb less than 1,000m (3,280ft) from the top due to a faulty oxygen regulator.
There are 41 teams with a total of 378 climbers permitted to scale Everest during the spring climbing season, assisted by an equal number of Nepalese guides.