The installation could help the tens of thousands of mountain climbers and trekkers who visit the Mount Everest region in the Solukhumbu district every year.
They have to depend on expensive satellite phones to remain in touch with their families as the remote region lacks proper communication facilities.
Nepali telecom company Ncell said its new facility is the first 3G setup at the base camp of Mount Everest, the world's tallest mountain at 8,850 meters (29,035 feet).
"This achievement is as mighty as the altitude as 3G high speed internet will bring faster, more affordable telecommunication services to the people living in the Khumbu Valley, trekkers, and climbers alike," said Lars Nyberg, chief of Nordic telecoms firm TeliaSonera, which owns 80 percent of the firm.
Ncell is a joint venture between local investors and TeliaSonera.
"Today we made the (world's) highest video call from Mount Everest," Ncell chief Pasi Koistinen told reporters in Kathmandu, referring to the call made from 5,300 meters (17,388 feet), the area from where climbers begin the actual climb to Mount Everest.
The facility provides fast surfing on the web, sending video clips and e-mails, as well as calls to friends and family back home at far cheaper rates than the average satellite phone, the company said in a statement.
Telecommunication services cover only a third of the 28 million people of Nepal, South Asia's poorest country.
Ncell said TeliaSonera would spend over $100 million to expand its facilities in Nepal next year and ensure mobile coverage to more than 90 percent of the Himalayan nation's population.