Local officials said the pair, who had started the hike on January 1, sent distress signals on Thursday due to heavy snowing and freezing temperatures in the heights of Mount Alam, in the Alborz Mountain range.
Rescue teams were immediately dispatched in helicopters to the site at of height of 4,700 meters, they said.
One of the climbers was, however, found dead and the other, who was severely affected by freezing, died amid the transfer operation.
Mount Alam is the second highest peak in Iran after Damavand, with an elevation of 4,805 meters, and supports permanent snow and glaciers.
The mountain, which sits near the Caspian Sea, is commonly known as the paradise of mountaineers due to its steep foothills, beautiful glaciers and snowfields and challenging technical routes.