The men, known as the “Hooded Men”, were interned without trial during the Troubles at a British Army base at Ballykelly in Co Derry.
The judges said the decision by the PSNI, made in 2014, was “irrational”.
The court also said the men’s treatment was “deplorable” and was “deliberate policy”.
Darragh Mackin, solicitor for one of the men, described the decision as “a landmark victory”.
The “Hooded Men” have long called for a new, independent investigation into their treatment.
In 2014, an RTÉ documentary unearthed fresh evidence, but the PSNI decided there was not enough evidence to warrant an investigation.
In 2019, Lord Chief Justice Sir Declan Morgan, then the North’s most senior judge, said their treatment “would, if it occurred today, properly be characterised as torture”.
Another of the three judges at the Court of Appeal in Belfast dissented with that conclusion.
The court was ruling on an appeal by police against a ruling that detectives should revisit the decision to end their inquiry.
In a statement, Assistant Chief Constable Jonathan Roberts said the PSNI acknowledged the court judgment and welcomed “the clarity it brings to some complex legal issues”.
“We recognise the difficult realities that victims, families, friends and broader society continue to deal with as a result of our troubled past,” he said.
“We will now take time to study today’s judgment around these complex legacy issues in detail and we will carefully consider its implications for future legacy investigations.
“If we are to build a safe, confident and peaceful society, then we must find a way of dealing with our past and we are committed to playing our part in that process.”
The Hooded Men say they were subjected to “deep interrogation” by the Army during their detention.The men said they were forced to listen to constant loud static noise; deprived of sleep, food and water; forced to stand in a stress position and beaten if they fell.
They also said they were hooded and thrown from helicopters a short distance off the ground – having been told they were hundreds of feet in the air.
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