The 25-year-old has been treated at the Mie General Hospital near Suzuka since losing control of his Marussia car and hitting the back of a tractor but has now been flown to Nice in France, his family said.
The Frenchman remains unconscious and in a critical condition, but "he is breathing unaided and his vital signs are stable".
Bianchi suffered a severe head injury when he collided with the vehicle that was removing Adrian Sutil's stricken Sauber, which had spun off the wet track a lap earlier.
The statement from his family said: "We are thankful that the next phase of Jules' treatment can continue close to home, where he can be surrounded and supported by his wider family and friends.
The Japanese Grand Prix began behind the Safety Car with drivers complaining over team radios they were unable to see through the spray. They were called back to the pits minutes later.
Following Sutil's crash on lap 42, yellow flags were waved before the corner to warn drivers of the incident.
The safety car was sent out after Bianchi's crash a lap later and the race was brought to an early end within minutes, with the rain getting heavier and the light rapidly deteriorating at Suzuka.
FIA race director Charlie Whiting said "a perfect storm" of conditions caused the accident.
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