Lawyers acting for the families said the conclusions, at the end of the longest jury case in British legal history, had completely vindicated their tireless 27-year battle for the truth.
The deaths were ruled accidental at the end of the original 1991 inquest.
But those verdicts were quashed following the 2012 Hillsborough Independent Panel report, which concluded that a major cover-up had taken place in an effort by police and others to avoid the blame for what happened.
The new jury concluded that blunders by the police and ambulance service on the day had “caused or contributed” to the disaster and that the victims had been unlawfully killed.
The jury forewoman wiped away tears and had a catch in her voice as she confirmed the answers to 14 questions about the disaster to coroner Sir John Goldring.
Leading Hillsborough campaigner Margaret Aspinall, whose 18-year-old son James died in the disaster, said afterwards: “Let’s be honest about this - people were against us. We had the media against us, as well as the establishment.
“Everything was against us. The only people that weren’t against us was our own city. That’s why I am so grateful to my city and so proud of my city.
“They always believed in us.”
Surrounded by a sea of camera crews and reporters outside the court, she added: “I think we have changed a part of history now - I think that’s the legacy the 96 have left.”
Labour MP Andy Burnham, who has supported the campaign, said: “This has been the greatest miscarriage of justice of our times.
“But, finally, it is over.”
The jurors were told they could only reach the unlawful killing determination if they were sure of four “essential” matters concerning the deaths at the 1989 FA Cup semi-final.
They had to be convinced match commander Chief Superintendent David Duckenfield owed a duty of care to those who died, 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 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 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 terrace crush had begun to develop;
• Policing of the match caused or contributed to a dangerous situation developing at the Leppings Lane turnstiles;
• Commanding officers caused or contributed to the crush on the terrace, as did those senior officers in the police control box when the order was given to open the exit gates at Leppings Lane;
• Features of the design, construction and layout of the stadium considered to be dangerous or defective caused or contributed to the disaster;
• Sheffield Wednesday’s then consultant engineers, Eastwood & Partners, should have done more to detect and advise on any unsafe or unsatisfactory features of the stadium.
On the question of the role of South Yorkshire Police in the emergency response, the jury said: “The police delayed calling a major incident so the appropriate emergency response was delayed.
“There was a lack of co-ordination, command and control which delayed or prevented appropriate responses.”
On the role of former South Yorkshire Metropolitan Ambulance Service (Symas), the jury said: “Symas officers at the scene failed to ascertain the nature of the problem at Leppings Lane.
“The failure to recognise and call a major incident led to delays in the responses to the emergency.”
Criminal investigations into the disaster and claims of corruption in its aftermath could finish by the end of the year, when prosecutors will decide whether to charge any individual or organisation.
The officer leading the police inquiry, Assistant Commissioner Jon Stoddart, said: “Now that the inquests have concluded, my sole focus is on completing the criminal investigation which I expect will be finished by the turn of the year.
“It will then be for the Crown Prosecution Service to consider the evidence and decide whether any individual or organisation should face criminal prosecution.”
The Independent Police Complaints Commission, the official police watchdog, also expects its investigation - the biggest in its history - to finish in December or January.
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 in court.
The fresh inquests began on March 31 2014 in a specially-built courtroom in Warrington, Cheshire.
After the key conclusions were delivered on Tuesday, someone in court shouted “God bless the jury”.
The jurors were given a round of applause as they left the courtroom.
Dozens of relatives of the victims have attended each of the more than 300 days the court has sat.
As families left the building they were met with applause from crowds who had gathered outside the court in support.
Many began singing Liverpool’s anthem You’ll Never Walk Alone.
At 4.10pm the court resumed for its final session, with the coroner thanking the jury and paying tribute to the families of the 96 - who responded by giving him a round of applause.
Sir John, addressing the jurors, said: “You have devoted over two years of your lives to these inquests.
“Your commitment and diligence has been remarkable.
“I suspect I speak for most when I say how hugely impressed we have been.
“Sitting on a jury in the shortest case is to perform a public duty of great importance.
“Sitting on a jury for this length of time in such a demanding and at times deeply moving case is to perform a public service of the highest order.
“It’s very important decisions in matters such as the Hillsborough disaster are taken not by lawyers but by members of the public such as you.
“I thank you very much indeed.”
At this point the families stood and applauded the coroner’s words.