The High Court has quashed the original inquest verdicts returned on 96 Liverpool football fans who died as a result of the 1989 Hillsborough disaster.
The Lord Chief Justice Lord Judge ordered new inquests after Attorney General Dominic Grieve's application.
Outside court, 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 on 15 April 1989.
Mr Grieve said he applied to the High Court as a result of the Hillsborough Panel's report, published on 12 September, which said 41 of those who died might have been saved.
He added Dr Bill Kirkup, the panel's medical member and a former associate chief medical officer at the Department of Health, had explained 58 of the dead "definitely" or "probably" had the capacity to survive beyond the 15:15 cut-off time.
New evidence undermined the coroner's summing-up, he said, adding later on BBC Radio 4's PM programme, that the report revealed "serious flaws" in the inquest.
He cited concerns about the timing of the fans' deaths, the role of the police and the false allegations that alcohol had played a material part in the tragedy, adding: "It [alcohol] was also used to blacken the reputation of the fans and potentially the victims, in a way that was very unfortunate, completely unacceptable and unfair."
Lord Judge said there was "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 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."
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 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 added.
Mrs May said former Durham Chief Constable Jon Stoddart would lead the new inquiry, focussing specifically on the Liverpool fans' deaths as a result of what happened at the 1989 FA Cup semi-final with Nottingham Forest.
Ninety-five fans died after they were crushed within two pens at the Leppings Lane terrace of Sheffield Wednesday's stadium, while the 96th died three years later after a Law Lords ruling stopping his tube feeding.
Mr Stoddart can recruit his own team but not any officers or former officers with any prior connection to the disaster or from West Midlands, South Yorkshire or Merseyside police forces.
He said his first priority was to meet with "as many of the families as possible" and to "establish a working open relationship with them".
The original inquest verdicts angered many bereaved families who were told at the 1990 hearing that all victims had been injured by 15:15 on the afternoon of the FA Cup semi-final between Liverpool and Nottingham Forest.
Evidence covering the response by the emergency services after this time was not heard.
Some relatives travelled to London for the hearing, while other family members and survivors watched on screens in Liverpool Family Court.
Damian Kavanagh, who attended the match and helped care for the injured, said the judgement was "massive".
"I never thought this day would come. It's uplifting to get to this stage and a serious wrong in society is going to be put right," he said.
"It's been an open wound for the city. We went through hell on that day and to get it turned around as if it was our fault, I can't describe it."
Margaret Aspinall, who lost her son, said something had "been achieved here today that's not been achieved before".
"It's took us 23 years to get this, we're not there yet but hopefully now we'll get there," she said.
"We have proved we were telling the truth all along - now we have to get the justice [the victims] deserve."
The Hillsborough panel's findings showed police and emergency services had made "strenuous attempts" to deflect the blame for the disaster on to the fans.
More than 160 police statements had been altered - 116 of them to remove or change negative comments about the policing of the match.