The government also set up a new police investigation into Britain's worst sporting disaster, in a victory for victims' families, who never accepted the official version of events and have campaigned for more than 20 years for 'Justice for the 96'.
Home Secretary Theresa May said an independent panel's report into Hillsborough had uncovered "truly shocking" evidence that must be investigated.
The Liverpool supporters died after a crush in an enclosed, overcrowded terrace at Sheffield Wednesday's stadium on April 15, 1989 during an FA Cup semi-final against Nottingham Forest.
An independent inquiry set up by the last government concluded in September that police tried to deflect the blame on to fans to cover up their own incompetence. It suggested 41 lives could have been saved if the emergency response had been quicker.
The original inquests found the deaths were "accidental". However, the government's chief legal advisor, Attorney General Dominic Grieve, applied to the court to quash those verdicts after the Hillsborough panel published its damning report.
Overturning the verdicts, Lord Chief Justice Lord Judge, the country's most senior legal authority, said there had been a "profound and palpable belief that justice has not been done and that it cannot be done without and until the full truth is revealed".
"We must record our admiration and respect for their determined search for the truth about the circumstances of the disaster... which - despite disappointments and setbacks - has continued for nearly quarter of a century," he said, according to the Press Association.
Grieve welcomed the ruling and said the original inquests had been "fundamentally unsound".
"I hope and trust that new inquests will provide a better understanding of how each of their loved ones died, and bring closer the justice for which they have fought so hard," he said.
The independent panel - set up in 2010 by the last Labour government to examine all the public paperwork relating to the tragedy - found that senior police edited their officers' statements from the day to try to limit the damage to their reputation.
Prime Minister David Cameron said in September that evidence suggesting police tried to defect the blame for the disaster onto Liverpool fans to cover up their own flawed response amounted to a "double injustice".
The tragedy shocked the world and led to a new era of modern stadiums across Britain. Banks of terracing and metal fences around pitches disappeared, replaced by seating and better security.
The new police investigation will be led by Jon Stoddart, a former chief constable of Durham police.
"The findings of the Hillsborough Independent Panel were truly shocking, but while the families have now been given the truth, they have not yet received justice," May said.
Campaigner Trevor Hicks, who lost two teenage daughters at Hillsborough, told the BBC the developments were a "huge step for the families".
"Justice is on its way - I think a lot of us are going to have a much happier Christmas," he said.
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