The Lord Chief Justice Lord Judge and two other judges in London quashed the original accidental death verdicts returned after 96 Liverpool football fans died in the crush 23 years ago - and ordered a fresh inquest.
At the same time, the Home Secretary announced a new police investigation into the Hillsborough disaster.
Former Durham Chief Constable Jon Stoddart will lead the new inquiry, which will focus specifically on the 96 deaths of Liverpool fans at the FA Cup semi-final in 1989.
The move comes after a damning report from the Hillsborough independent panel laid bare a cover-up which attempted to shift the blame for the tragedy on to its victims.
Home Secretary Theresa May said: “I am determined to see a swift and thorough response to the findings of the Hillsborough Panel to deliver justice for the 96 football fans who died and the families who have fought so hard on their behalf.”
More than 40 families who had travelled to London for the hearing burst into applause when the judges granted an application brought by the Government’s top law officer, Attorney General Dominic Grieve.
Lord Judge, announcing that there were “good grounds” for the application, described what happened in 1989 as “catastrophic”.
Referring to the families, many of whom were weeping in court, he said there had been a “profound, almost palpable belief that justice has not been done and that it cannot be done without and until the full truth is revealed”.
He said: “We must record our admiration and respect for their determined search for the truth about the circumstances of the disaster and why and how it had occurred, which - despite disappointments and setbacks - has continued for nearly quarter of a century.”
When giving the ruling, Lord Judge expressed regret that the process the families had gone through over the years since the disaster had been “so unbearingly dispiriting and prolonged”.
The Lord Chancellor Chris Grayling said: “The victims’ families and survivors of the Hillsborough tragedy have seen their cause take another important step forward today.
“I will now do everything I can to help to get new inquests established quickly.
“I have received a request from the Doncaster and Bradford coroners for a judge to be appointed to conduct these inquests and I am today asking the Lord Chief Justice to make a recommendation to me on suitable candidates as soon as possible.”
Trevor Hicks, chair of Hillsborough Family Support Group, spoke of his delight at the decision to quash the inquest verdicts.
Speaking outside the Royal Courts of Justice, he said: “Justice is on its way. Everything we’ve said has been proven to be correct.”
Michelle Carlile, 44, clutching a photograph of her brother Paul, 19, who died at Hillsborough, said of today’s decision: “It is bitter-sweet. We have known the truth for 23 years.”
Mayor of Liverpool Joe Anderson said after the decision: “This is a watershed moment on the road to justice for the families of the 96, and I share their overwhelming relief that, after 23 very painful years, the inquest verdicts have been quashed.
“It is the only right and proper decision that the High Court could make in the wake of the overwhelming and compelling evidence uncovered by the Hillsborough Independent Panel.
“We must all keep up the pressure that has driven the momentum over the last few months to make sure that the families get the justice they deserve.
“I also welcome the new police investigation, which we all hope will result in those that played a role in causing the disaster and the monumental cover-up are brought to account.”
Lord Judge said each of those who died in the tragedy was a “helpless victim of this terrible event”.
He ruled that it was in the interests of justice to hold a fresh inquest.
He said the “interests of justice must be served” - “however distressing the truth will be brought to light”.
The main plank of the Attorney General’s application related to crucial new medical evidence.
Welcoming the decision, Mr Grieve said: “Thanks to the work of the Hillsborough Independent Panel it was made clear that the medical evidence underpinning the original inquests, and relied upon in subsequent reviews and inquiries, was fundamentally unsound.
“In addition, the statements concerning the actions of the police and emergency services, and the original evidence concerning the alcohol consumption of the deceased, give rise to questions that fresh inquests should address.
“I therefore believe the interests of justice require the 96 inquests to be quashed and for new ones to be held.
“Today, the Court has agreed with me.
“These processes inevitably take time, but I share the hope that the new inquests are held speedily as possible and I know that efforts are being made to expedite them.
“The families’ long and painful quest for the truth reached a breakthrough with the publication of the Hillsborough Independent Panel report.
“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.”
Around a dozen Hillsborough victims’ relatives and friends watched a live link to the events at the Royal Courts of Justice from Courtroom 27 in the Liverpool Civic and Family Court.
Speaking outside the court after the hearing, the family of Hillsborough victim Gary Jones, 18, said today was a major step forward.
Mr Jones’s sister, Cathy, said she was “delighted” by the words of the Lord Chief Justice.
She said: “It’s a step towards justice and the truth. The last 23 years has been very difficult - every day having to fight. Nobody should have to justify why somebody has died and have to fight for their honour.”
Marion Brady, whose son Paul, 21, was killed, said it was “absolutely wonderful” that a new police investigation had been instigated, and added: “It’s been very hard. We have had knockback after knockback. I just hope I live to see it all come to fruition.”
Ian Daley, 48, who was at Hillsborough and lost his friends Graham Wright, 17, and Gordon Horn, 20, said: “The truth is out now. It’s only what the families deserve. They’ve had to wait for a long time.”
Stephen Kelly lost his brother Michael, 38, in the disaster, describing him as “38 going on 15”.
He said: “I’m absolutely over the moon. It’s a brilliant result today, we’ve justified our actions for all these years.
“We’ve really worked hard for this, and Hillsborough wasn’t an accident, it was a disaster waiting to happen.
“But it’s been proven today and the inquest has been quashed. I’m really pleased with that.
“It’s clearly been stressful at the least, but we got here, and everybody who supported us all these years - this is for them.”
Andy Burnham, Labour MP for the North West constituency of Leigh, has been instrumental in championing the Hillsborough victims’ plight.
Today, he was visibly moved as he celebrated and hugged family members outside the Royal Courts of Justice.
He agreed that helping to overturn the inquest findings was one of his best achievements and the difference he made was one of the reasons why he came into politics.
He applauded the Hillsborough families for their enduring determination and strength of character.
He said: “Starting this process off three years ago, we couldn’t have hoped then that it would come to this.
“It is unbelievable what the families have been through.
“For them to get on a coach in Liverpool at 5am and come down to London and be told what they should have been told 23 years ago says so much about their determination.”
Anne Williams, 60, whose 15-year-old son Kevin died at Hillsborough, has been one of the loudest voices throughout the campaigners’ efforts for justice.
Suffering from cancer, she attended today’s proceedings in a wheelchair.
She applauded Attorney General Dominic Grieve as “a man of his word”.
“He did what he promised,” she said.
“I am glad we never gave up. It has been hard, but we wouldn’t have been here today.
“I’d like a corporate manslaughter verdict in the inquest, it’s the least for what they have done.
“It’s a long process.
“God willing, I will be here, it has been a long wait to see justice.
“I am so glad I could be here today to hear it for myself.”
Referring to the cover-up that shifted blame away from the authorities and on to the victims, she said: “I can’t forgive them the extremes they went to.
“Why didn’t they just give us the truth?
“The way they twisted and turned things, like the lies I was told about Kevin being dead by 3.15pm when he died at 4pm...
“This hasn’t sunk in yet.
“I keep thinking somebody is going to step in and ruin it.”