The Court of Appeal ruled that the guilty verdict returned against Brian Shivers was unsafe because no finding was made on when he allegedly became aware of the murder plot.
Shivers will now remain in custody until the Public Prosecution Service decides whether to seek a retrial.
The 47-year-old, from Magherafelt, Co Londonderry, was challenging his conviction for the murders of Sappers Mark Quinsey, 23, and 21-year-old Patrick Azimkar.
Speaking from her home in London, Geraldine Azimkar said Tuesday's decision has left their family disillusioned with the criminal justice system.
"It seems scandalous really that this terrible murder happened and the attempted murders happened and it looks like no one is going to be held to account for it," Mrs Azimkar said.
We feel very let down by the criminal justice system. It does not seem to work for the victims of crime.
"It is the failure of the criminal justice system, which is very highly loaded in favour of the defendant and therefore against the interests of victims and their loved ones.
"We feel there is no justice and it is going to be very hard to get peace in Northern Ireland when they see there is no justice.
"The whole thing is awful from start to finish."
The victims were gunned down by the Real IRA as they collected pizza at the gates of Massereene Barracks in Co Antrim in March 2009. The shootings were carried out hours before the soldiers were due to be deployed to Afghanistan.
Last February, Shivers was ordered to serve a minimum 25 years in prison for his part in the killings.
He was also found guilty of six counts of attempted murder and one of possession of two firearms with intent to endanger life.
His co-accused, Colin Duffy, a 45-year-old republican from Lurgan, Co Armagh, was acquitted of all charges, including the two murders.
Shivers, who suffers from cystic fibrosis and has only a few years to live, was originally found guilty as a secondary party who aided and abetted by setting fire to the getaway car.
DNA analysis had established a link to matches found in the partially burnt-out Vauxhall Cavalier used by the gunmen.
But Shivers' lawyers argued that it was legally impossible for him to be convicted of murder because there was no actus reus, or criminal act, prior to the murder.
Delivering judgment on Tuesday, Lord Chief Justice Sir Declan Morgan said the trial judge had not dealt with the concept of a joint enterprise.
"The issue for the court was whether it should be inferred that there was a common enterprise to which the appellant agreed prior to the attack to carry out a shooting attack with intent to kill," Sir Declan pointed out.
We do not accept that a person who provides assistance after a murder with full knowledge of what has happened thereby becomes guilty of murder.
Sir Declan Morgan
Sir Declan, sitting with Lord Justices Higgins and Girvan, held that the test applied by the trial judge required no knowledge of the attack until a rendez-vous with the gunmen.
"The learned trial judge made no findings as to when the appellant had the relevant knowledge."
He added: "We conclude, therefore, that the appeal must be allowed."
Lawyers were told that a slot was available next month at Belfast Crown Court for a possible retrial.
Counsel for the PPS is expected to confirm on Wednesday whether it is seeking fresh criminal proceedings.
A spokesperson said: "The PPS will inform the Court of Appeal of its decision whether or not it's seeking a retrial."
Shivers, who maintains his innocence, appeared by prison video link to hear the outcome of his appeal. His lawyer said he was relieved by the verdict but expressed concerns about his health.
Niall Murphy, of Kevin R Winters and Co, said: "This is example of the justice system working, however we are gravely concerned at our client's ongoing acute medical condition.
"He has been admitted to hospital for 56 days across three separate admissions since the hearing of his appeal in May and he is routinely refused access to his medication.
"Mr Shivers has been through a terrible ordeal whereby he has been repeatedly assaulted /abused whilst in prison and in hospital where he is continuously under armed guard."
He added: "Mr Shivers looks forward to the end of this ordeal and hopes that this judgement is the first step towards that."
A Ministry of Defence spokesman spokesman said: "Our thoughts remain with the families of Sappers Patrick Azimkar and Mark Quinsey at this extremely difficult time."