Bianchi, 25, had been fighting for his life under controlled medical conditions in the Centre Hospitalier Universitaire hospital in his home city of Nice, southern France.
He is the first Formula One driver to die from a racing accident since triple world champion Aryton Senna lost his life in San Marino in 1994.
“Jules fought right to the very end, as he always did, but today his battle came to an end,” the Bianchi family said in a statement posted on Facebook in the early hours of Saturday.
“The pain we feel is immense and indescribable.”
French President François Hollande paid tribute to the gifted Marussia driver.
“French motorsport has lost one of its greatest hopes,” Hollande commented in a statement.
Formula One supremo and the sport's chief executive Bernie Ecclestone stated: “It was so sad to hear the news about Jules. We are now going to miss a very talented driver and a really nice person. We must not let this ever happen again.”
Bianchi joined Marussia in 2013 and competed in 34 grands prix, notching two world-championship points — still the team's best score.
John Booth, team principal of Marussia, now called Manor F1, said: “Words cannot describe the enormous sadness within our team this morning, as we come to terms with losing Jules. He has left an indelible mark on all our lives, and will forever be part of everything we have achieved, and everything we will strive for going forward.”
Bianchi suffered a traumatic brain injury when his car careered off the rain-drenched Suzuka circuit during the Japanese Grand Prix on October 5 and smashed into a recovery truck at around 200 kilometres (125 miles) an hour.
Bianchi's death ended a promising career that he hoped would see him join the elite ranks of Ferrari, something the young driver said he felt “ready” to do three days before the race in Japan.
Hopes for his recovery had been fading and on Monday, his father Philippe said he was “less optimistic” that Jules would make a full recovery after spending nine months in hospital with no signs of “significant progress”.
Racing in his genes
Bianchi's crash, which came as Formula One legend Michael Schumacher was battling back from a horrific ski accident, added to anxiety surrounding the high-octane motor racing circus.
While yellow warning flags were up, racing was still intense when Bianchi spun off and experts said the wet track, his tyres and his speed could all have been to blame for the accident.
Questions have also been raised about whether the marshals should have halted the race after Adrian Sutil's Sauber came off the track on the previous lap.
Bianchi's accident led to new safety measures to ensure drivers slowed down for on-track incidents, including the implementation of a 'virtual safety car'.
Born in Nice in 1989 to Italian parents, Bianchi had racing in his genes. His grandfather Mauro had been a well-known Formula Three and endurance driver in the 1960s.
His father Philippe for years managed a karting track near the Paul Ricard circuit near Marseille, in southern France, where Jules made his debut as a race car driver.
But his death also recalled another tragic piece of family history: his grand uncle Lucien, who competed in 17 grands prix, was also killed in a crash while racing in 1969 at the age of 34.
The Bianchi family in their Saturday statement thanked “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” and asked for privacy.
Bianchi is the fourth leading French sports figure to perish in 2015, following the deaths of sailor Florence Arthaud, boxer Alexis Vastine and Olympic swimming champion Camille Muffat.