The High Court has quashed the original accidental death inquest verdicts returned after 96 Liverpool football fans died in the crush at Hillsborough 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.
The application came as Home Secretary Theresa May announced there would be a new police investigation into the disaster, led by former Durham Chief Constable Jon Stoddart, which will focus specifically on the 96 deaths.
Lord Judge said there were "good grounds" for the application made by Grieve and described what happened in 1989 as "catastrophic".
Referring to the families, 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."
After Lord Judge announced the decision of the court, families in the packed courtroom greeted it with a loud round of applause. More than 40 families had made the journey to London for the hearing, while others watched by videolink from Liverpool.
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".
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".