Cantonal police on Wednesday said the man died on Tuesday at the hospital in Sion.
The man received serious head injuries, despite the fact he was wearing a helmet, after falling and hitting a rock while skiing on Monday with a group in the Orzival region in an area known as Creux du Varnec, police said.
The group had been skiing on a forestry road when the victim for an unexplained reason quickly changed direction and fell.
He was transported by helicopter in critical condition.
Vercorin, at 1,350 metres, is a ski resort near Sierre, served by lifts that rise to an altitude of almost 2,400 metres.
The Orzival area is not directly served by any lifts.
The accident occurred a day after an avalanche elsewhere in Valais claimed the life of another British skier.
The body of the 39-year-old man, who was also a Swiss citizen, was found on Tuesday in the Col de Forclaz area following a lengthy search, Valais police said.
He was buried in three metres of snow after an avalanche 200 metres long and 50 metres swept him away.
The man was identified by Britain's Evening Standard newspaper as Chris Longbottom, originally from London but working in Switzerland.
Longbottom was skiing off piste with a group of five other skiers at an altitude of around 1,900 metres.
The other skiers, including two from Holland and three Swiss, were able to dig themselves out.
A rescue team of 30 people involving two helicopters and dog teams searched for the man in an effort that was interrupted by bad weather, police said.