The High Court has quashed the original accidental death inquest verdicts returned after 96 Liverpool fans died in the Hillsborough disaster 23 years ago.
The Lord Chief Justice Lord Judge and two other judges in London ordered fresh inquests following an application by the Attorney General Dominic Grieve.
Earlier on Wednesday home secretary Theresa May announced a new investigation would be held into the 1989 tragedy.
Lord Judge said there were "good grounds" for the application made by Mr Grieve and described the tragedy as "catastrophic".
A large round of applause from the families in the packed courtroom greeted the announcement. More than 40 families had made the journey to London and others watched the hearing via a videolink.
When giving the ruling, Lord Judge expressed how "unbearingly dispiriting and prolonged" the torment had been for the families of those who perished.
He paid tribute to the tireless families of the victims, saying: "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."
The Lord Chief Justice Lord Judge added 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".
Trevor Hicks, chair of the Hillsborough Family Support Group, spoke of his delight at the High Court's decision and proclaimed: "Justice is on its way.
"Everything we've said has been proven to be correct."
Michelle Carlile, who clutched a photograph of her brother Paul, who died at Hillsborough aged 19, labelled the decision "bittersweet".
"We have known the truth for 23 years," she added.
James Saunders, managing director of Saunders Law Ltd, the solicitor who represents the Hillsborough Family Support Group, said: "Those who caused the deaths, concealed what happened, lied to the press and denigrated the victims to hide their own culpability may expect to be brought to account in court."