A new police inquiry into the disaster was also announced.
Their fight for the truth took a historic step forward when a panel of three High Court judges, headed by the Lord Chief Justice Lord Judge, quashed the original accidental death verdicts returned after 96 Liverpool football fans died in the crush 23 years ago - and ordered a fresh inquest.
The unopposed, "exceptional" application to the court was made by the Government's top law officer, Attorney General Dominic Grieve.
It follows the publication in September of a damning report laying bare a cover-up which attempted to shift the blame for the tragedy onto its victims.
The Liverpool supporters died at Sheffield Wednesday's Hillsborough stadium on April 15, 1989, where their team faced Nottingham Forest in an FA Cup semi-final.
Today, the High Court judges ruled that it was "necessary, desirable and in the interests of justice" that a fresh inquest should be held.
Their decision came as a new police investigation into the disaster was announced by Home Secretary Theresa May.
Former Durham Chief Constable Jon Stoddart will lead the new inquiry.
The Home Secretary 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."
Following the High Court's decision, 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."
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 as 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."
Trevor Hicks, chair of the Hillsborough Family Support Group, spoke of his delight at the High Court's decision, saying: "Justice is on its way. Everything we've said has been proven to be correct."
Lord Judge, referring to the families - many of whom were weeping in court - 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".
Lord Judge said each of those who died in the tragedy was a "helpless victim of this terrible event".
He said: "Our earnest wish is that new inquests shall not be delayed for a moment longer than necessary."
Mayor of Liverpool Joe Anderson described the decision as a "watershed moment on the road to justice" for the families.