The 38-year-old man died almost instantly, after leaping from the well-known take off spot La Mousse, near Lauterbrunnen.
He was with his two pals shortly before he took the plunge.
Berne police told The Sun they were investigating the exact circumstances of the jump and the British Embassy has been informed of the tragedy.
It is not known if the man was wearing a parachute or a wing suit.
A local cafe worker said: ''It's quite a testing jump and you have to be very skillful.
"We heard the chopper going up and then someone told us there had been a fatality. It's very sad.''
The Swiss base jumping association has classified the leap at La Mousse, near Launterbrunnen, as "red" on its website.
He is the second Brit to have died in the Alps this summer. Last month Robert Haggarty, 48, from Hampshire, died in an accident over the border in Italy.
Base jumping is one of the most dangerous recreational activities in the world, with a fatality and injury rate 43 times as high as parachuting from a plane.
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