Jeremy Salvesen, part of the well-known Salvesen business dynasty, was killed after veering off the slopes at a popular ski resort.
Mr Salvesen, of the global business family, fell 17 feet on to a rock on a run at the resort of La Clusaz. Police said he was not wearing a helmet.
The tragedy echoes the skiing accident in December that left Michael Schumacher in a coma.
The Formula One star remains in hospital in Grenoble.
Mr Salvesen, 51, who lived in Elie in Fife, was flown by helicopter to Annecy General Hospital where he was pronounced dead on Thursday.
It was said he had been skiing down a relatively easy slope at speed.
One report said that he had been skiing with his son when the accident happened but this has not been confirmed.
Mr Salvesen was a member of the broad empire created by the famous late shipping magnate Christian Salvesen.
His family spoke of their loss and said they would take some comfort from knowing he had been doing something he loved.
In a statement, they said: "We are devastated by Jeremy's death as a result of catastrophic injuries in a tragic accident in the French Alps while he was skiing on a beautiful day with a large family group.
"We all take comfort from knowing that he was doing something he loved with a big smile on his face.
"As always, Jeremy was pushing himself to the limit. His life has been a wonderful adventure and we treasure all our memories of him.
"We want to thank everyone at La Clusaz and at Annecy who did everything they could for Jeremy and in particular, we want to thank the expert medical professionals who cared for him."
No further comment is expected to be made by the family.
He had been involved in a number of businesses including the online Groovy Chocolate firm, as well as other ventures such as round-the-world yachting.
Jeremy Salvesen pursued a number of ventures and as he chased new goals had described himself as an "unsuccessful chartered surveyor".
Five years ago he took part in a round-the-world yachting race in his 40-foot boat.
He moved to rescue the famous sweet-makers Duncan's in Edinburgh in 1996 which had employed 3000 people at the height of its success.
A spokeswoman for La Clusaz Municipal Police said: "He was skiing on the easy-going blue slope. It appears he lost control of his skis.
"He was going very fast and there was nothing wrong with the slope.
"He was not wearing a helmet."
The death is the latest to affect the French skiing industry, with several incidents reported this year including three in one day in March.
A spokeswoman for the Foreign and Commonwealth Office said consular assistance had been offered to Mr Salvesen's family.
The spokeswoman said: "We are aware of the death of a British national on April 10 in France.
"We are providing consular assistance to the family at this difficult time."
Tributes were being planned in the village of Elie.
Friends at one pub in the village told how the community had been struck by Mr Salvesen's death.