Cameron said that Attorney General Dominic Grieve will review the report as quickly as possible in order to decide whether to apply to the High Court to quash the original, flawed inquest and order a new one. It will be for the court to make the final decision.
Today's report showed that the Hillsborough families had suffered a "double injustice", both in the "failure of the state to protect their loved ones and the indefensible wait to get to the truth", and in the efforts to denigrate the deceased and suggest that they were "somehow at fault for their own deaths".
Cameron told MPs: "With the weight of the new evidence in this report, it is right for me today as Prime Minister to make a proper apology to the families of the 96 for all they have suffered over the past 23 years.
"On behalf of the Government - and indeed our country - I am profoundly sorry for this double injustice that has been left uncorrected for so long."
The Prime Minister added: "What happened that day - and since - was wrong.
"It was wrong that the responsible authorities knew Hillsborough did not meet minimum safety standards and yet still allowed the match to go ahead.
"It was wrong that the families have had to wait for so long - and fight so hard - just to get to the truth.
"And it was wrong that the police changed the records of what happened and tried to blame the fans.
"We ask the police to do difficult and often very dangerous things on our behalf, and South Yorkshire Police is a very different organisation today from what it was then.
"But we do the many, many honourable police men and women a great disservice if we try to defend the indefensible.
"It was also wrong that neither Lord Justice Taylor nor the Coroner looked properly at the response of the other emergency services."
Cameron said that the Hillsborough disaster was "one of the greatest peacetime tragedies of the last century".
The evidence uncovered by today's report was "deeply distressing" and raised "vital questions which must be examined", he said.
Announcing that the report will be debated in the House of Commons soon after MPs return from their conference break in October, Cameron said: "The conclusions of this report will be harrowing for many of the families affected.
"Anyone who has lost a child knows the pain never leaves you.
"But to read a report years afterwards that says - and I quote - 'a swifter, more appropriate, better focused and properly equipped response had the potential to save more lives', can only add to the pain."
And he added: "Not enough people in this country understand what the people of Merseyside have been through.
"This appalling death toll of so many loved ones lost was compounded by an attempt to blame the victims.
"A narrative about hooliganism on that day was created which led many in the country to accept that it was somehow a grey area.
"Today's report is black and white.
"The Liverpool fans 'were not the cause of the disaster'.
"The Panel has quite simply found 'no evidence' in support of allegations of 'exceptional levels of drunkenness, ticketlessness or violence among Liverpool fans', 'no evidence that fans had conspired to arrive late at the stadium' and 'no evidence that they stole from the dead and dying'."
The Prime Minister paid tribute to "the incredible strength and dignity of the Hillsborough families and the community which has backed them in their long search for justice".
Cameron quoted the findings of the report on "the failure of the authorities to help protect people; the attempt to blame the fans; and the doubt cast on the original coroner's inquest".
He told MPs: "There is a trail of new documents which show the extent to which the safety of the crowd at Hillsborough was 'compromised at every level'."
"The report backs up again the key finding of the Taylor Report on police failure," said Cameron. "But it goes further by revealing for the first time the shortcomings of the ambulance and emergency services response.
"The major incident plan was not fully implemented. Rescue attempts were held back by failures of leadership and co-ordination. And, significantly, new documents today show there was a delay from the emergency services when people were being crushed and killed."
Cameron said that the Hillsborough families were "right" in their belief that some of the authorities "attempted to create a completely unjust account of events that sought to blame the fans for what happened".
But he said that the report had found "no evidence of any government trying to conceal the truth".
Cameron said: "At the time of the Taylor Report the then prime minister (Margaret Thatcher) was briefed by her private secretary that the defensive and - I quote - 'close to deceitful' behaviour of senior South Yorkshire officers was 'depressingly familiar'.
"And it is clear that the then government thought it right that the Chief Constable of South Yorkshire should resign.
"But... governments then and since have simply not done enough to challenge publicly the unjust and untrue narrative that sought to blame the fans."
The Prime Minister also cited evidence from the report showing that some of those who died "could have had potentially reversible asphyxia beyond 3.15pm in contrast to the findings of the Coroner and a subsequent Judicial Review".