Alvaro Bulto, 51, died in the Bernese Oberland region, known as a mecca for base jumping, on Friday morning.
His identity was revealed by El Mundo, the Spanish newspaper.
For reasons not immediately known his parachute failed to open, Bern cantonal police and the local prosecutor’s office said in a news release.
Bulto died immediately after hitting the ground in the Stechelberg area of Lauterbrunnen, police said.
He was in the Swiss Alpine region with several friends.
Bulto, born in Barcelona, was the son of Paco Bulto, founder of the Bultaco and Montesa motobike companies, El Mundo reported on the weekend.
In addition to his sporting and TV activities, he was known for living the life a jetsetting celebrity.
In the early 1990s he had a two-year relationship with Princess Cristina.
Early this summer he had a close call during base the world base jumping championships in Benidorm, Spain.
He has reportedly tried to fly over the Gran Hotel Bali with the intent of landing on a nearby beach.
However, a problem with his parachute meant he crash-landed on the hotel roof, leaving him with minor injuries.