"I am glad we never gave up. It has been hard," Williams said. "God willing, I will be here, it has been a long wait to see justice."
The wrongdoing and mistakes that led to the crush at Liverpool's match against Nottingham Forest were fully exposed in September after an independent panel examined previously secret documents.
The papers uncovered a sophisticated attempt by police to shift blame onto Liverpool fans watching from a standing-room-only section, by instructing officers to change statements and insinuate many fans were drunk and had histories of violence or criminality.
"I can't forgive them the extremes they went to," Williams said. "Why didn't they just give us the truth?"
Many of the fans died due to lack of attention from police and emergency services after about 2,000 supporters were herded by officers into caged-in enclosures that were already full at Sheffield Wednesday's ground.
British Prime Minister David Cameron apologized in September for errors by authorities, and now the official cause of the fans' deaths looks set to change on their death certificates.
"It is bittersweet," said Michelle Carlile, whose 19-year-old brother Paul died at Hillsborough. "We have known the truth for 23 years."
Lord Chief Justice Igor Judge and two other judges decided that fresh inquests should be held.
Igor Judge 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."
Steve Rotheram, a legislator representing part of Liverpool, described the verdict as marking "the beginning of the end of the Hillsborough disaster."
In Britain, an inquest is held to determine the facts whenever someone dies unexpectedly, violently or in disputed circumstances.
Inquests do not determine criminal liability, but as the hearing was being held, the government announced those deemed responsible for the disaster could now face criminal prosecution.
Jon Stoddart, who recently retired as chief constable of the Durham force, will lead the new police inquiry, which will also work with the previously announced investigation by the country's police watchdog into officers' conduct.
"My role is to ensure that we determine exactly what happened in the lead-up to and on the day of the disaster and establish where any culpability lies," Stoddart said.
Home Secretary Theresa May said she wants to "deliver justice" for the fans who died and their families.
"I am determined to see a swift and thorough response to the findings of the Hillsborough Panel," she said.
The disaster led to the introduction of all-seat stadiums for leading clubs in England.
- AP