Drake, 33, was in a coma since Saturday, when he and two other divers jumped from a helicopter with plans to glide into a valley in the Alps, but instead crashed in a pasture, police said. Dan Vicary of New Zealand, 33, and Ludovic Worth, 34, were killed in the incident.
Wingsuit divers wear jumpsuits that add surface area to their bodies, enabling them to glide like a bird for several minutes after a jump, before opening a parachute. The Swiss Alps are a popular location for wingsuit and other extreme sport attempts.
Swiss police did not identify drake by name in reporting the death, but the World Wingsuit league, on its Facebook page, named him and established a page in his honor.
Drake was among the biggest names in the wingsuit community, and traveled around the world for competition and exhibitions.
The investigation into the accident continues, police said.