The 44-year-old South Korean fell to his death at around 11.00pm on Friday as he was making his descent from the Eiger, and rescuers found his body during the night.
He and two compatriots had reached the mountain's summit on Friday and were descending its west face.
The other two climbers were rescued unscathed by helicopter on Saturday morning.
The 28-year-old BASE-jumper, who was with five other people, died after making a jump from the Kandersteg Classic in Gastern. After his parachute opened, he crashed into the side of the mountain several times before falling onto a rocky promontory.