Eric Larsen and his team took advantage of a brief lull in the weather to push for the summit of the world's highest peak on October 15, the tourism ministry said.
The successful climb means Larsen has now reached the North and South Poles and Mount Everest in a single calendar year, a goal he set himself in 2009 with the aim of raising awareness of the impact of global warming.
"We made it. The Sherpas and I did it. It's hard to believe," he said from the summit in an audio clip posted on his website, www.ericlarsenexplore.com.
There are two climbing seasons for Everest, but most mountaineers favour the spring, when weather conditions on the 8,848-metre (29,028-foot) Himalayan peak tend to be more favourable.
Larsen said the group had taken advantage of a three-day window of good weather for their ascent, but he described the weather conditions on their way down the mountain as "brutal" and said he had barely slept in four days.
Tourism ministry spokesman Laxman Bhattarai said there were just two expeditions on Everest this season. The other, a Japanese climber attempting a solo ascent, was forced to abandon his attempt due to bad weather.
Around 3,000 people have climbed Everest, which straddles Nepal and China, since it was first conquered by Edmund Hillary and Tenzing Norgay in 1953.
Some 250 people made it to the summit from the more popular south side in Nepal during this year's spring climbing season, which begins in late April and ends in late May, mountaineering officials have said.