Gerry McGowan, Michael Toner, Stephen Crumlish and Gerard Kelly were teenagers when they were charged with killing Lieutenant Steven Kirby.
The so-called Derry Four are from Circular Road in Derry.
They fled to the Republic of Ireland until their acquittal in 1998.
They have been involved in a civil case against the police for wrongful arrest.
Their solicitor said that the out-of-court-settlement comes with “no acceptance of liability” on the part of the police.
PSNI Assistant Chief Constable George Clarke said police “acknowledge there were significant shortcomings in the treatment of the men involved in this case and we recognise the distress that this has caused them.”
“Policing has developed greatly since these incidents took place, as have our policies and procedures for dealing with detained persons.”
Mr Clarke said detainees have a range of protections afforded by the Police and Criminal Evidence (NI) Order and Human Rights legislation.
He added: “PSNI has strict human rights compliant policies and procedures in place to ensure that its custody facilities and all investigative processes comply with the highest possible standards.”
In a statement read out at a press conference, Gerry McGowan said: “We thank our families who have endured this painful injustice with us over the past 40 years.
“This compensation will not undo the years of hurt and pain inflicted on us and our families, however, it allows us to look to the future and# we feel some sense of closure that the state is finally acknowledging their wrongdoing.
“Finally we would like to thank the people of Derry who have stood by us over the past 40 years and never doubted our innocence.”
At the time of their arrests, two of the men were 17 years of age and two were 18.
They were detained in Strand Road police holding centre at the time for up to three days, according to their solicitor.
“During that detention period they had no access to lawyers, legal advice, parents or family members,” she said.
“While in police detention in these oppressive circumstances, all four young men signed false confessions in relation to the murder of Lt Stephen Kirby on 14 February 1979 at Wapping Lane at the bottom of Abercorn Road.
“They also signed false confessions in relation to four knee-capping incidents in Derry for which no other persons had been charged or prosecuted.
“My clients were entirely innocent of all these offences.”
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