Mr Murney, 30 and from Derrybeg Terrace in Newry, stood trial earlier this year on seven counts of publishing, collecting and possessing information likely to be of use to terrorists between August 2011 and July 2012.
He was accused of publishing on his Facebook page photographs of police officers on duty.
During the Diplock, non-jury trial held at Belfast Crown Court, the prosecution said the photographs were found on a computer, together with two videos on an iPhone, during a police search of his south Down home in November 2012.
Mr Murney took photographs of police officers in June 2012, as the Olympic torch passed through the city. He also took images of officers who were policing a protest in support of Republican prisoners and against searches in Maghaberry prison which were taking place at the time.
He was part of this protest and was the press officer for Éirígí, who organised the demonstration. He later published the images on his Facebook page.
Mr Murney also published photographs in August 2011 and July 2012 of himself being stopped and searched by police, as well as collecting and making a record of the policing of a 12th of July parade in Newry, which showed the faces of officers present.
My imprisonment for the past 14 months was as a direct result of my political views and my membership of Éirígí - an open and legitimate political party.
During the trial, the court heard that when Mr Murney's home was searched in November 2012, photographs of police officers on duty in Newry and Belfast were found, along with a minute-long video of a police operation on the A1 where a bus believed to be carrying explosives was stopped and searched.
When asked during the trial why he recorded the bus incident, Mr Murney said the bus had children on board and he was asked by parents of the children if Éirígí could be of assistance, adding it was his intention to capture on camera what was happening.
Giving evidence at his trial, Mr Murney denied the photographs and videos were for terrorist purposes, stating he had them to report what was going on, in his role as press officer.
When asked about the images of him being stopped and searched, Mr Murney made the case that he was recording the incidents to show the Committee on the Administration of Justice as he believed he was being harassed by the PSNI.
In her ruling, Judge Corrinne Philpott said: "There is no evidence before this court that Éirígí supports violence, or has argued for violent action to be taken against the police, or that the organisation is directly linked to those that support terrorist activity."
She said: "The prosecution must prove beyond reasonable doubt that the accused possessed information likely to be of use to terrorists and that he had no reasonable excuse for his actions.
"In the view of this court, the prosecution have not discharged that burden to the requisite standard, that is beyond reasonable doubt, and therefore the accused is entitled to an acquittal on all counts."
As the Judge made her final remark, family, friends and supporters of Mr Murney clapped in the public gallery.
Speaking outside the court, Mr Murney thanked his legal team, described his period in custody as "internment on remand" and vowed to continue his work as a press officer with Éirígí.
In a statement issued on his behalf, Mr Murney said: "Those charges, of which I have been found to be innocent, were brought against me by the PSNI, who objected to the fact that I recorded, documented and publicised PSNI personnel abusing the human and civil rights of citizens in the Newry area."