Crilly, 60, from South Armagh, had denied murdering the Grenadier Guardsman in May 1977.
In one of the most infamous killings of the Troubles, Captain Nairac was abducted from a bar in Drumintee before being shot dead.
Mr Justice Richard McLaughlin said: “The prosecution has not proved beyond reasonable doubt the state of knowledge or intention necessary to transform the transporting of (Liam) Townson (who was convicted of the murder) by Crilly to an unspecified place at an unspecified time into a knowing participation in a potential murder. For these reasons I find the accused not guilty.”
He was cleared on all five charges, including kidnapping and false imprisonment as well as murder, after he was accused of dropping off the killer.
Following Capt Nairac’s death, Crilly, from Lower Foughill Road, Jonesborough, went to the US for 27 years, using his birth name Declan Power.
The prosecution claimed that, following the kidnapping of Capt Nairac from the Three Steps Inn, Crilly, then 26, picked up the gunman, Liam Townson, who was later convicted by the Special Criminal Court in Dublin.
Crilly had been asked about the killing by BBC Spotlight journalists.
The judge said: “The admissions by Crilly to the journalists from the Spotlight programme prove he was involved to some degree in the events surrounding the death of Captain Nairac.
“He was present at the Three Steps Inn where what he described as a ‘battle’ took place. This can only mean what he witnessed was the abduction of Captain Nairac but it does not prove his active participation in it.”
He said the evidence did not prove where Capt Nairac was when Crilly went to collect Townson or when he dropped him off, nor does the evidence establish when or by whom the decision was made to kill him.
“I have concluded that the prosecution has not proved Crilly was a participant in the abduction,” the judge added.
Besides the Spotlight interview, during which Crilly expressed concern that he would be jailed, much of the evidence centred on hair, believed to be that of the Grenadier Guardsman, which was discovered pulled out by the roots near the suspected murder scene at Ravensdale Forest, Co Louth, and in a Cortina car belonging to Crilly’s family. A large clump of hair was found in the car.
The judge added: “Given that the prosecution has been unable to prove a sufficient nexus between Crilly and the Cortina, the significance of the mass of hair found in it becomes irrelevant in proof of participation by Crilly in the murder or abduction.”