After hearing evidence for two years, jurors concluded that policing decisions at the ill-fated match in 1989 "caused or contributed" to the deaths, and amounted to "gross negligence".
Relatives of the victims have fought a 27-year campaign to get to the heart of what happened during the disaster, and were incensed by a 1991 inquest ruling the deaths were accidental.
There were shouts of "Yes!" in court today when the jury's verdicts were delivered, with people jumping to their feet. Many emerged from the courtroom hugging and in tears.
"We have had two years of hell going up and down to the court each day, but the only thing I can say at the end of it today: it has been well worth it," said Margaret Aspinall, whose 18-year-old son James died at the stadium in Sheffield, northern England.
Also Read
Prime Minister David Cameron hailed the "tireless bravery" of campaigners who had pursued the truth.
"All families and survivors now have official confirmation of what they always knew was the case -- that the Liverpool fans were utterly blameless in the disaster," he said in a statement.
But the Crown Prosecution Service (CPS), England's state prosecutors, said it would consider whether to bring charges once ongoing investigations conclude, probably by the end of the year.
The disaster occurred on April 15, 1989 during an FA Cup semi-final between Liverpool and Nottingham Forest.
Seeking to alleviate a crush that had developed outside the ground shortly before kick-off, David Duckenfield, the senior officer in charge of policing the event, ordered the opening of an exit gate.
Duckenfield, now 71 and retired, admitted at the inquest that he told a "terrible lie" in the immediate aftermath of the match by claiming that fans had stormed the gate.
The inquest, which began in March 2014, took place in Warrington, northwest England, 25 kilometres outside Liverpool.
One juror was discharged as she suffered a nervous breakdown after sitting through all the evidence in Britain's longest-ever inquest.
John Goldring, a retired judge who presided over the hearings, asked the nine-member jury to decide on 14 key points, with the issue of whether the victims were unlawfully killed the central question.