The two men -- identified by the Indian embassy as Paresh Nath and Goutam Ghosh -- were near the summit of the 8,848-metre (29,029-foot) mountain on Saturday when they lost contact with the rest of their team.
"Rescuers located Paresh Nath's body around the South Col (mountain pass)," Wangchu Sherpa of Trekking Camp Nepal told AFP.
The cause of Nath's death has not yet been established.
But the South Col -- located at an altitude of 8,000 metres -- marks the beginning of the "death zone", notorious for its difficult terrain and thin air, as low levels of oxygen raise the risk of altitude sickness.
"There is too much wind and snow to continue our search for Goutam Ghosh today," Sherpa said.
The missing climbers were part of a team of four, one of whom -- Subhash Pal -- died after falling ill on Sunday. The fourth team member, a woman, was rescued and taken to hospital.
Subhash Pal was the third mountaineer to die on Everest in recent days after an Australian and a Dutch climber succumbed to altitude sickness.
Some 400 people, including more than 150 foreigners, have summited Everest this season after two consecutive years of deadly disasters that led to almost all attempts being abandoned.
Hundreds of climbers fled Everest last year after an earthquake-triggered avalanche at base camp killed 18 people.
Only one climber reached the top in 2014 after an avalanche killed 16 Nepali guides that year.
Despite the risks and recent disasters, Everest's allure remains undimmed, with Nepal issuing 289 permits to foreigners for this year's spring climbing season, due to end soon.
Mountaineering is a major revenue-earner for the impoverished Himalayan nation.
The wave of successful summits is expected to give a boost to the climbing industry, left reeling after a string of disasters, including last year's quake, which killed almost 9,000 nationwide.