The Prime Minister has offered "a profound apology" to grieving relatives who have waited 23 years to see their loved ones cleared of blame for the tragedy that unfolded at Sheffield Wednesday's stadium in 1989.
Mr Cameron was making a Commons statement as the Hillsborough Independent Panel, chaired by the Bishop of Liverpool the Rt Rev James Jones, published its report into the tragedy.
It found the police made "strenuous attempts" to deflect the blame for the disaster on to innocent fans.
The panel oversaw the release of previously unpublished papers from about 80 organisations including the government, police, emergency services, Sheffield City Council and the South Yorkshire coroner.
The Prime Minister told MPs that police changed statements and tried to blame Liverpool supporters for the crush on the Leppings Lane terrace as their team prepared to play their FA Cup semi-final against Nottingham Forest on April 15, 1989.
Mr Cameron said on Wednesday: "The families have long believed that some of the authorities attempted to create a completely unjust account of events that sought to blame the fans for what happened.
"The families were right. The evidence in today's report includes briefings to the media and attempts by the police to change the record of events."
Victims' families also disputed the findings of an inquest into the deaths, which ruled all the victims were dead or brain dead by 3.15pm and which subsequently recorded verdicts of accidental death.
Mr Cameron said the panel's report backed the relatives' concerns and he ordered Attorney General Dominic Grieve to consider today's findings and decide whether to apply to the High Court for new inquests.