Strange, 23, had found fame at age 17 when he became the youngest person to climb the so-called Seven Summits, referring to the highest peak on each continent.
On Thursday afternoon, Strange jumped from a 2,000 metre summit in the Swiss canton of Uri wearing a wingsuit, a piece of equipment that resembles human-size bat wings.
He crashed into the ground, likely after losing control mid-jump, authorities in Uri said.
Police said he made the jump shortly after 12pm when conditions were reportedly windy, adding that a further investigation would be launched.
The average wingsuit jump lasts barely a minute and within eight seconds, the jumper reaches speeds of 200 kilometres per hour (120 miles per hour).
A video from 2014 of Johnny Strange performing a wingsuit jump
Aside from Strange, perhaps the most prominent wingsuit-related casualty was the August 2013 death of Mark Sutton, the James Bond parachutist from the opening ceremony at the London Olympics.
The films released by jumpers with GoPro cameras attached to their heads are almost impossible to watch, with the jumpers seemingly having no control as they descend at extraordinary speeds, often slipping through narrow mountain passages.
But enthusiasts say the focus on danger and death undermines the incredible skill and preparation required of a successful jump.
A 2011 image of Johnny Strange. Photo: Jason Merritt/ Getty Images North America/AFP