The Saville Inquiry into the Bloody Sunday killings has found the actions of British soldiers was "both unjustified and unjustifiable".
In a statement to the House of Commons, the Prime Minister said the inquiry found the order that sent British soldiers into the Bogside "should not have been given".
Mr Cameron said the report found none of those killed by British soldiers was armed with firearms and no warning was given by the soldiers.
The casualties were down to the soldiers "losing their self control", said Mr Cameron - who told MPs: "I am deeply, deeply sorry."
The Prime Minister said the tribunal found some soldiers had "knowingly put forward false accounts".
Families of the Bloody Sunday dead had been allowed to read the inquiry's findings before they were made public.
They had marched on the Guildhall in Londonderry where they sifted through the pages that exonerated their loved ones.
After Mr Cameron's statement to MPs, families came outside and were greeted by applause from crowds of people.
The 14 civilians died after British troops opened fire on a civil rights march in Londonderry on January 30, 1972.
The Saville inquiry is the longest and most expensives in British legal history, containing 30 million words of testimony and costing close to £200 million.