In a statement in the House of Commons, Cameron said that the Hillsborough Independent Review has provided evidence that police attempted to change the record of events, with 164 police statements significantly amended, that emergency services suffered "major shortcomings" and that fans were incorrectly blamed of having a role in the events.
The Prime Minister spoke of a "double injustice" - for the tragedy itself, which occurred at the start of an FA Cup semi-final between Liverpool and Nottingham Forest on April 15 1989, and the failure to investigate it properly in the aftermath.
"What happened that day - and since - was wrong," Cameron said. "It is right for me as Prime Minister to make a proper apology.
"There are no grey areas. Today's report is black and white. The Liverpool fans were not to blame for the disaster."
A report into the disaster by Lord Justice Taylor, published in 1990, found that the main reason for the disaster was a failure of "police control" but the Crown Prosecution Service decided there was insufficient evidence to bring a prosecution.
The victims' families say it is an injustice that no individual or organisation has been held fully accountable for the disaster. They believe a major incident plan was never initiated by South Yorkshire Police and fans in the Leppings Lane end at Sheffield Wednesday's Hillsborough stadium were denied emergency medical attention.
The families also dispute the findings of an inquest into the deaths, which ruled that the victims were all dead, or brain dead, by 3.15pm and which subsequently recorded a verdict of accidental death.
They were the first to see thousands of official documents relating to the disaster for the first time on Wednesday, a release of 400,000 pages - from around 80 organisations including the Government, police, emergency services, Sheffield City Council and the South Yorkshire coroner - overseen by the Hillsborough Independent Panel.
Later, the documents will be uploaded to a website for viewing by the general public.
A report explaining the contents of the documents will be published by the panel, chaired by the Bishop of Liverpool, the Rt Rev James Jones.
The independent panel, set up in 2010 by the last Labour Government to examine all the public paperwork relating to the tragedy, concluded that it could have been avoided, more lives could have been saved and the police response was flawed.
"There were clear operational failures in response to the disaster and in its aftermath there were strenuous attempts to deflect the blame onto the fans," it said.
Senior police edited their officers' witness statements from the day to paint them in a less damaging light, the report said. South Yorkshire Police removed negative comments from 116 out of 164 statements.
Three relatives of the victims fainted when they heard that the panel put forward evidence of a cover-up, apparently vindicating their 23-year campaign to find 'Justice for the 96'.
"There were two disasters at Hillsborough - one on the day and one afterwards," said Trevor Hicks, who lost two daughters in the disaster. "There was a contrived, manipulated, vengeful and spiteful attempt to divert the blame."
Barrister Michael Mansfield, who helped the victims' families, said he believed the police's behaviour was part of the biggest cover-up in British legal history and the report could lead to prosecutions within months.
"The system failed miserably," Mansfield said in a news conference at Liverpool's imposing Church of England cathedral.
Former Labour Justice Secretary Charles Falconer said the report showed a "concerted conspiracy to withhold the truth by public bodies", while Liverpool Football Club chairman Tom Werner said "the world has heard the real truth about what happened".
South Yorkshire Police said "grave errors had been made".
"I am shocked by it and so are my senior people. If people are shown to have acted criminally, then they should face prosecution," Chief Constable David Crompton told the BBC.
The press secretary of then Conservative Prime Minister Margaret Thatcher incensed families at the time by blaming the disaster on a "tanked-up mob".
The report found no reason for the coroner's decision to take blood alcohol samples from all of the victims, including children.
"The pattern of alcohol consumption among those who died was unremarkable," the report said. "The weight placed on alcohol levels was ... inappropriate and misleading."
While inquiries found hooliganism played no part in the disaster, the police crowd management plan was preoccupied with preventing disorder, the report said.
Liverpool fans had been tainted by the Heysel stadium disaster in Belgium in 1985. Fighting inside that stadium led to Juventus fans being crushed against a wall that collapsed. Six Liverpool fans and 33 supporters of the Italian team died.
The real danger at Hillsborough lay in the emergency services' poor planning and a stadium that failed to meet minimum safety standards, the report said.
Its capacity was overstated and previous crushes at Hillsborough had been ignored.
Sheffield Wednesday have also issued an apology.
"Chairman Milan Mandaric and the current board of directors have adopted a policy of complete compliance with the requests of the Hillsborough Independent Panel and on behalf of the club would like to offer our sincere condolences and an apology to all the families who have suffered as a consequence of the tragic events of 15 April, 1989," it read.
The disaster was also one of the low points for Rupert Murdoch's British newspaper group, currently reeling from a phone hacking scandal that has led to criminal charges against former senior executives and reporters.
Many in Liverpool still boycott Murdoch's newspapers after the top-selling Sun accused their fans of stealing from the dying, urinating on policemen and beating up an officer giving the kiss of life. On Wednesday, Kelvin Mackenzie, the editor who published those false allegations, issued an apology.
Relatives rejected his comments as "too little, too late" and began a news conference by asking any journalists from The Sun to leave the room.