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.
Bishop Paul Bayes told Premier it had been "a very long journey for the people of Liverpool".
He said: "The fans have been exonerated from blame and that for our city is a huge thing.
"People have really struggled for so many years to try and shine some light on what happened and today I think that light has been shone."
He added that it was "not acceptable" that it had taken 27 years to get justice.
"I'm not saying that justice was deliberately hidden or covered up, there may have been some of that, it's not for me to say, but it's not right that people should have had to spend the thick end of 30 years trying to get justice for their loved ones.
"I'm delighted for the families."
The Hillsborough disaster unfolded during Liverpool's cup tie against Nottingham Forest on April 15th as thousands of fans were crushed at Sheffield Wednesday's ground.
Chief Superintendent David 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 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.
The fresh inquests began on March 31st, 2014, in a specially-built courtroom.
The 1991 accidental deaths verdicts from the original inquests were quashed following the 2012 Hillsborough Independent Panel, which concluded that a major cover-up had taken place in an effort by police and others to avoid the blame for what happened.
After the key conclusions were delivered on Tuesday, someone in court shouted "God bless the jury".
Bishop Paul said he had always been praying for those involved that "the love of Jesus Christ will touch them in their grief".
"My prayer for the Hillsborough families, for everybody in our region is that God's love and light will continue to shine and that all those in pain will be comforted".
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.
Bishop Paul Bayes speaking to Premier's Antony Bushfield:
