The former cabinet minister, widely credited with helping to secure a new inquest into the disaster, said in a statement: “This has been the greatest miscarriage of justice of our times.
“But, finally, it is over. After 27 long years, this is real justice for the 96, their families and all Liverpool supporters.
“The survivors of this tragedy can finally be remembered for what they were on that day - the heroes of Hillsborough who tried to help their fellow fans.”
Mr Burnham, the MP for Leigh, added: “The Hillsborough Independent Panel gave us the truth. This Inquest has delivered justice. Next must come accountability.
“For 27 years, this police force has consistently put protecting itself above protecting those hurt by the horror of Hillsborough. People must be held to account for their actions and prosecutions must now follow.
“Disgracefully, lawyers for retired police have attempted to continue the cover-up in this courtroom. They made it an adversarial battle in defiance of the Lord Chief Justice’s ruling. This has been brutal on the Hillsborough families and put them through hell once again.
“The current leadership of South Yorkshire Police needs to explain why it went back on its 2012 apology at this Inquest, prolonging the agony for the families.
“The sense of relief we feel is tempered by the knowledge that this day has taken far too long in coming. The struggle for justice has taken too great a toll on too many. But the Hillsborough families have at long last prevailed and finally their loved ones can rest in peace.”
Steve Rotheram, Labour MP for Liverpool Walton, said: “I have waited 27 years for this moment. But I know it comes too late for many. I was there on the day and saw the horror unfold before my very eyes.
“Before we’d even buried our dead, the hurt of loss was compounded by the lies and smears. I remember picking up a newspaper and feeling sick to the pit of my stomach. They inflicted terrible pain on a city at its moment of maximum grief.
“I’ve seen how friends have suffered. This is a momentous day but they should never have had to wait so long. The truth is out there for all to see. Justice has been served by the verdicts and now it is about accountability.”
Prime Minister David Cameron said the inquests had provided official confirmation that Liverpool fans were “utterly blameless” in the disaster,
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.
In a statement, the PM 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.”