Emily Watts, 26, from Suffolk in UK, crashed into a snowdrift and suffered a heart attack near Chamonix on Saturday.
Ms Watts, also known as Mimi, was taken to a hospital in Annecy and placed on a life support machine.
The French authorities have confirmed she died on Thursday and said it would be assisting the family, who had travelled to France.
Ms Watts is said to have been an experienced snowboarder who had been working in France for a few weeks.
She was in the Grands Montets, the largest ski resort in the Chamonix Valley, on the first day of the season when the accident happened.
Her family had said mountain rescuers and police had told them Ms Watts caught an edge of the piste and "was catapulted into a 70cm (27in) pile of powder".
Another skiier raised the alarm but Ms Watts is thought to have suffered a cardiac arrest by the time emergency crews arrived.
