The 96 Liverpool fans who died in the Hillsborough disaster were unlawfully killed, the inquests jury has concluded.
The jurors were told they could only reach that determination if they were sure of four "essential" matters concerning the deaths at the 1989 FA Cup semi-final.
They had to be convinced that overall match commander Chief Superintendent David Duckenfield owed a duty of care to those who died in the disaster, and that he was in breach of that duty of care.
Thirdly, they would need to be satisfied that his breach of duty caused the deaths and, fourthly, that it amounted to "gross negligence".
They concluded it was unlawful killing by a 7-2 majority.
The conclusion was greeted with sobbing and cheers at the hearing in Warrington.
The jury also ruled that fan behaviour did not cause or contribute to the tragedy.
The Hillsborough disaster unfolded during Liverpool's cup tie against Nottingham Forest on April 15 as thousands of fans were crushed at Sheffield Wednesday's ground.
Mr Duckenfield gave the order at 2.52pm to open exit Gate C in Leppings Lane, allowing around 2,000 fans to flood into the already packed central pens behind the goal.
The jury also found that both the police and the ambulance service caused or contributed to the loss of lives in the disaster by an error or omission after the crush in the west terrace had begun to develop.
After the key conclusions were delivered, someone in court shouted "God bless the jury".
The jurors were given a round of applause as they left the courtroom.
Lawyers acting for relatives of the victims said the jury's conclusions had completely vindicated the bereaved families' tireless 27-year fight for justice.
The jury of six women and three men gave their decisions on an emotionally charged day for relatives of the 96, many of whom were at court for the conclusion of the longest jury proceedings in British legal history.
Last Wednesday the jury indicated to the court in Warrington that unanimous decisions had been reached on every question apart from question six - unlawful killing.
They were given a majority direction yesterday and quickly indicated they had reached a majority decision on the outstanding question.
The fresh inquests began on March 31, 2014, in a specially built courtroom in Warrington.
The 1991 accidental deaths verdicts from the original inquests were quashed following the 2012 Hillsborough Independent Panel report after a long campaign by the families of the dead.
Dozens of relatives of the victims have attended each of the more than 300 days the court has sat at Bridgewater Place on the Cheshire town's Birchwood Park business park.
At the start of the inquests, the coroner said none of the victims should be blamed for their deaths.
Emotional tributes to each of the 96 were then delivered by family members in the form of personal portraits.
The jurors also found unanimously that policing of the match caused or contributed to a dangerous situation developing at the Leppings Lane turnstiles.
Commanding officers also caused or contributed to the crush on the terrace, the jury decided, as did those senior officers in the police control box when the order was given to open the exit gates at the Leppings Lane end of the stadium.
As families left the building they were met with applause from crowds who had gathered outside the court in support.
Many had arrived wearing Liverpool Football Club scarfs and holding posters and banners of loves one.
Labour MP Andy Burnham, who has supported the families' campaign, said: "This has been the greatest miscarriage of justice of our times.
"But, finally, it is over."
Former Liverpool captain Jamie Carragher tweeted: "Justice finally. #JFT96."
John Aldridge, who was in the Liverpool at Hillsborough, tweeted: "Fantastic to see the reaction of the families outside the court! Very emotional as well.
"The truth is out AT LAST. Take note all the doubters!!"
The Hillsborough inquests have provided official confirmation that Liverpool fans were "utterly blameless" in the disaster which claimed 96 lives, Prime Minister David Cameron has said.
Mr Cameron paid tribute to the "tireless bravery" of survivors and victims' families in pursuing the truth. The landmark ruling was "long overdue" after 27 years of waiting, he said.
Home Secretary Theresa May is due to give the Government's response to the inquest jury's unlawful killing finding in an oral statement to the House of Commons on Wednesday.
In a statement, Mr Cameron said: "Today is a landmark moment in the quest for justice for the 96 Liverpool fans who died on that dreadful day in April 1989.
"It is also a long overdue day. The bereaved families and survivors of the Hillsborough disaster have had to wait 27 long years for the full facts of what happened and it is only due to their tireless bravery in pursuing the truth that we arrived at this momentous verdict.
"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 that unfolded at Hillsborough."