The news was posted on Bianchi's official Twitter feed early on Saturday morning French time and later confirmed by the Manor F1 team.
Bianchi, 25, had been in a coma since the October 5 accident, in which he collided at high speed with a mobile crane which was being used to pick up another crashed car.
The family statement said "Jules fought right to the very end, as he always did, but today his battle came to an end. The pain we feel is immense and indescribable."
The Manor team tweeted: "We are devastated to lose Jules after such a hard-fought battle. It was a privilege to have him race for our team."
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Bianchi died at the Centre Hospitalier Universitaire in his hometown of Nice, where he had been since his emergency treatment in Japan in the days after the accident.
"We wish to thank the medical staff at Nice's CHU who looked after him with love and dedication," the family statement said. "We also thank the staff of the General Medical Center in the Mie Prefecture (Japan) who looked after Jules immediately after the accident, as well as all the other doctors who have been involved with his care over the past months.
Bianchi's accident occurred at the end of the race at Suzuka. In rainy, gloomy conditions, Bianchi's car slid off the track and ploughed into a crane picking up the Sauber of German driver Adrian Sutil, who had crashed out at the same spot one lap earlier.