Bianchi, 25, who died on last night, 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 perish from a racing accident since triple world champion Aryton Senna 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 today.
The gifted young Marussia driver's death sparked a flood of tributes from his pitlane colleagues and the world of politics.
"French motorsport has lost one of its greatest hopes," French President Francois 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."
World champion Lewis Hamilton summed up the sombre mood from the grid, the Mercedes star declaring on Twitter: "A sad, sad day today, guys. Please pray for Jules' loved ones. RIP Jules. God bless."
John Booth, team principal of the team 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.
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