'Shot in back'
Relatives of those killed were given copies of the report in advance of its public release.
The investigation looked into the events of January 30, 1972 when 13 men who were marching at the time were shot dead by the troops.
A fourteenth man later died from his injuries, while another 15 people were wounded in the incident.
Troops had charged crowds massing for the illegal Catholic demonstration in Bogside, a hostile city neighbourhood.
They said that they had been responding to shooting by the Irish Republican Army and were striking at armed individuals in the group.
However, no soldiers suffered injuries.
"The soldier who killed my brother shot him in the back," said Joe McKinney, one of the 56 people given the report amid tight security inside Derry's city hall.
"My brother was unarmed. That's murder, plain and simple."
In the original probe by British authorities in the same year as the deaths, some of those killed were alleged to have been bombers or gunmen>
Relatives have expressed confidence that the report by Mark Saville, a UK judge, will make clear their innocence.
Mickey McKinney, whose 27-year-old brother was killed in the events, said the British army and government must be held to account.
"We want the truth - a declaration of innocence and a recommendation that those responsible are prosecuted," he said.
"If I know justice has been done, I'll be able to move on and know I did my best."
Victims' families held a procession to Derry city hall before the release of the report on Tuesday, holding pictures of those killed and injured.
During Northern Ireland's four decade conflict, 1972 was to become one of the deadliest years following Bloody Sunday.
About $285m has been spent on producing the report.