The 34-year-old was in intensive care in a Swiss hospital and an MRI scan detected bleeding on the brain.
His mount Boomerang Bob was brought down and fatally injured in the race.
The Injured Jockeys Fund said: "In due course George will leave the intensive care area to the rehabilitation wing of the Wellington Hospital."
Jockey George Baker has returned to England for treatment in London after his heavy fall on a frozen lake track in St Moritz, Switzerland last month.