The team was trying to blaze a new route on the south face of Mount Gurja, Yonhap news agency said. The 7,193 metre-high peak (23,600 feet) is located roughly 216 km (135 miles) northwest of Nepal's capital, Kathmandu.
Their bodies were found on Saturday near their base camp about 3,500 metres (11,500 feet) above sea level.
The disaster appeared to be caused by a "sudden gust of wind," Lee In-jung, chairman of the Union of Asian Alpine Associations, told reporters.
"I believe it might be the first time in the history of climbing the Himalayas that an accident was caused this way," he said, adding it could deter people from climbing there.
Lee said the belongings of the climbers, including footage from a documentary filmmaker on the team, had not been fully recovered.
A joint funeral ceremony is expected to be held at Kim's alma mater, the University of Seoul, on Friday, according to Yonhap.