The 25-year-old had been in a coma since crashing his Marussia car into a recovery vehicle in wet conditions in Suzuka last October.
His family said: “Jules fought right to the very end, as he always did, but today his battle came to an end.”
Marussia, now known as Manor, said the team was “devastated”.
Bianchi died in hospital near his parents’ home in Nice in the south of France.
His family said: “We thank Jules’s 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.
“Listening to and reading the many messages made us realise just how much Jules had touched the hearts and minds of so many people all over the world.”
Bianchi made his F1 debut with Marussia in 2013 and was also a member of the Ferrari young driver academy after previously working as a test driver for the team.
The Manor team : “We are devastated to lose Jules after such a hard-fought battle. It was a privilege to have him race for our team.”
The accident happened when Bianchi’s car slid off the track and into a crane picking up German driver Adrian Sutil, who had crashed at the same spot one lap earlier.
A working group of the sport’s governing body, the FIA, investigated the accident and found that as Bianchi went off the track into the run-off area, he “applied both throttle and brake together, using both feet” over-riding the fail-safe mechanism. His front wheels had also locked.
It also said that Bianchi “did not slow sufficiently to avoid losing control.”
