The victim, whose death marked the latest in a string of base jumping fatalities in Switzerland, was a 44-year-old man from Texas, Vaud cantonal police said.
He died after jumping from the Sex Rouge mountain on Friday around 4pm, according to a statement.
The victim was with a 46-year-old German who made a successful jump from the 2,971-metre-high peak after the pair took the Glacier 3000 cable car to get there, police said.
The American had problems with his takeoff and crashed with full force into a cliff face 100 metres below before falling a further several hundred metres, the force said.
His fall ended in a couloir that was difficult to access, police said.
Operations to recover the body with a helicopter began on Friday and resumed on Saturday, when because of poor weather and visibility they had to be put off until Sunday.
Police have not disclosed the identity of the victim.
Both men who jumped from Sex Rouge were wearing wingsuits designed to allow users to “fly” before opening a parachute.
The fatal accident is fifth involving base jumpers in Switzerland in the past month.