The High Court has quashed the original inquest verdicts returned on 96 Liverpool football fans who died in the 1989 Hillsborough disaster.
The Lord Chief Justice Lord Judge ordered fresh inquests following an application by the Attorney General.
Trevor Hicks of the Hillsborough Family Support Group said it was "a huge step for the families".
The home secretary has also announced a new police inquiry into the disaster.
Theresa May said the new inquiry would re-examine what happened in April 1989.
New medical evidence was used as a basis for the new inquests application.
Dominic Grieve made his request to the High Court three months after a new report established 41 of those who died might have been saved.
Mr Grieve said the application was being made as a consequence of the Hillsborough Panel's report published on 12 September, which he said was a "remarkable" document.
He said that Dr Bill Kirkup, the medical member of the panel and a former associate chief medical officer at the Department of Health, had explained that, of the deceased, 58 "definitely" or "probably" had the capacity to survive beyond the 15:15 cut-off time.
That new evidence, which Mr Grieve said formed the "essential basis" for his application "undermines the coroner's summing-up at the inquests".
In making his judgement, Lord Chief Justice Lord Judge said there had been "deliberate misinformation surrounding the disaster".
"There has been a profound and palpable belief that justice had not been done [and] it is clear there are sound grounds for this application," he said.
He added that the court wanted to "record our admiration and respect [to the families] for their determined search for the truth about the disaster and why and how it had occurred, which - despite disappointments and setbacks - has continued for nearly quarter of a century."
The judgement was applauded by the families of some of the victims in the court.
Speaking outside, Mr Hicks, who lost two daughters in the disaster, said the families "couldn't have written it better".
"It's clear now justice is on its way - I think a lot of us are going to have a much happier Christmas," he said.
Justice Secretary Chris Grayling said he would 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," he said.
Mrs May said former Durham Chief Constable Jon Stoddart would lead the new inquiry, which will focus specifically on the 96 deaths of Liverpool fans as a result of what happened at the FA Cup semi-final in 1989.
The fans died after they were crushed within two pens at the Leppings Lane terrace of Sheffield Wednesday's stadium during the semi-final with Nottingham Forest on 15 April 1989.
Mrs May said she was "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".
Mr Stoddart will be able to recruit investigators and staff to his team, but he will not be allowed to employ officers or former officers with any prior connection to the Hillsborough disaster or from the West Midlands, South Yorkshire or Merseyside police forces.
He said he was "aware of the great significance and personal responsibility which comes with leading this criminal investigation".
"My first priority is to meet with as many of the families as possible and to establish a working open relationship with them throughout the investigation," he said.
South Yorkshire Police Chief Constable David Crompton said the force, which policed the game in 1989, would "continue to co-operate fully with any judicial processes".