Jean Andre Quemener, from Jersey, was killed after reportedly losing control of his wingsuit during high winds in the Italian Dolomites at Canazei, north of Venice, according to The Sun.
It is claimed the 32-year-old hit rocks before falling more than 200m (656ft) to his death.
A spokesman from the Foreign Office said: "We are supporting the family of a British man following his death in Canazei, Italy, and are in contact with the local authorities."
Base jumpers are able to fly at speeds of up to 120mph before opening a parachute and gliding to the ground.
However, the rates of fatalities and injuries are about 50 times higher than skydiving, and almost 200 base jumpers died between 1981 and 2012.
Last year, another British man, Robert Haggarty from Hampshire, died in the Dolomites region after launching himself from the Castelletto Della Busazza mountain.
The 47-year-old, who had completed 500 jumps previously, suffered multiple injuries when he failed to clear a cliff ledge.