News of his death was posted on Bianchi’s official Twitter feed 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.”
Bianchi competed in 34 races over the 2013 and 2014 seasons, scoring the first championship points for Manor - then known as Marussia - by finishing fifth at last year’s Monaco Grand Prix.
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.”
Bianchi died at the Centre Hospitalier Universitaire in his home town 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 Centre 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.
“Furthermore, we thank Jules’ colleagues, friends, fans and everyone who has demonstrated their affection for him over these past months, which gave us great strength and helped us deal with such difficult times.”
Bianchi’s accident prompted F1 to alter its safety regulations and stop racing more quickly under caution-flag conditions.
The family statement was issued by his parents Philippe and Christine, his brother Tom and sister Melanie.
Bianchi’s accident happened at the end of the race at Suzuka. In rainy, gloomy conditions, his car slid off the track and smashed into a crane picking up the Sauber of German driver Adrian Sutil, who had crashed out at the same spot one lap earlier.
The section of the track where the accident occurred was subject to double yellow flags from race stewards, due to Sutil’s crash. But they failed to prevent a second accident.
A working group of the sport’s governing body, the FIA, investigated the accident and found that as Bianchi went off track into the run-off area, he “applied both throttle and brake together, using both feet” and thus overriding the failsafe mechanism. His front wheels had also locked.
It also said that Bianchi “did not slow sufficiently to avoid losing control”.
The findings of the working group prompted F1 to alter its rules, allowing a “virtual safety car” in which race stewards can neutralise a race, forcing all cars to proceed slowly into the pit lane.
The start times of some races were also moved forward to prevent them continuing in dim light conditions.
Bianchi’s family has already lost a member in a crash. In 1969 his great-uncle Lucien Bianchi died in an accident during testing at the Le Mans race track when he crashed his Alfa Romeo into a post, a year after winning the prestigious endurance race.
His death came only days after Philippe Bianchi had said his son would not have wanted to go on living if he was severely disabled.
“If he had a severe handicap, we are convinced that is not what Jules would want,” he told France Info radio on Monday.
“We talked about it. He discussed with us that if one day he had an accident like that of Michael Schumacher, that even if his only handicap was not being able to drive, he would have a lot of difficulty living. Because it was his life.”