"Home time today," the former Formula One racer said on his Twitter feed before posting a photograph of himself on a stretcher next to a medical plane flying him to Oxford.
"You've been cruel once again Le Mans but I'll stand on your top step one day."
Davidson, 33, suffered two broken vertebrae on Saturday night after a collision with a slower Ferrari he was trying to lap at the Sarthe circuit sent his Toyota flying through the air and into the tyre barriers.
Doctors have put his recovery time at three months.
Davidson said following the crash he hoped to be fully mobile again after three weeks.