Sean Hoey was found not guilty on all charges
Sean Hoey, 38, of Molly Road in Jonesborough, was found not guilty of a total of 58 charges, including those not directly linked to the bombing.
Speaking at Belfast Crown Court, Mr Justice Weir was critical of police evidence and said they were guilty of a "deliberate and calculated deception".
He said transcripts of the trial had been sent to the police ombudsman.
In delivering his verdict, Mr Justice Weir referred to "a most disturbing situation exposed by the defence".
The judge said he was not satisfied beyond reasonable doubt that prosecution submissions showed that all explosive devices were made by one person.
Mr Justice Weir said there had been calculated deception by the police
Speaking after Thursday's verdict, Mr Hoey's solicitor, Peter Corrigan, said his client was an innocent man who had been completely vindicated.
"Today's judgement - a reasoned, lengthy and well considered judgement - completely vindicated this position that he maintained. Sean Hoey is an innocent man," he said.
Outside the court, Mr Hoey's mother Rita said: "I want the world to know that my son Sean Hoey is innocent.
"The authorities north and south have held two separate trials, but one witch-hunt."
It was concluded that the evidence was sufficient to provide a reasonable prospect of obtaining a conviction
Public Prosecution Service
Reaction to Omagh verdict
Lawrence Rush, whose wife Elizabeth died in the explosion, said the case had been handled disastrously by the police.
"I wouldn't have liked the wrong man to be charged," he said.
Michael Gallagher, whose son Aidan was killed in the bombing, said a cross-border inquiry into the bombing should be set up by the British and Irish governments.
'Consider judgment fully'
A police statement said they would study Mr Justice Weir's judgement in detail and would work to ensure that any organisational or procedural shortcomings were addressed.
"We also await the outcome of a police ombudsman investigation into two officers who gave evidence during the trial," it said.
The Public Prosecution Service said the decision to prosecute Sean Hoey was made following a careful analysis of the available evidence.
The LCN DNA results were challenged by defence experts who claimed that the scientific community is 'divided' over whether the technique itself is reliable
DNA at heart of case
Stan Brown, chief executive of Northern Ireland's Forensic Science Service, said it was now important "to take time to consider the judgment fully".
At the heart of the case were the bomb timers used in the attacks. Forensic scientists had examined them for both fibres and Low Copy Number (LCN) DNA.
LCN is a relatively recent development of DNA science which allows analysis of tiny samples of skin cells, sweat and other bodily fluids.
The prosecution claimed that the forensic examination had shown links to the south Armagh electrician.
One of their expert witnesses claimed the chances of the DNA being anyone other than Mr Hoey's were "one in a billion".
But the LCN DNA results were challenged by defence experts who claimed that the scientific community is "divided" over whether the technique itself is reliable.
Lawrence Rush was highly critical of the police case
It is believed police spent a total of £16m on their investigation.
The verdict was delivered after a trial which lasted a total of 56 days over a period of 10 months.
It was one of the biggest murder trials in UK legal history.
In addition to the 29 counts of murder, Sean Hoey was also charged with five counts of conspiracy to murder, four counts of conspiracy to cause an explosion, six counts of causing an explosion and 12 counts of possession of explosive devices.
This photo was taken shortly before the explosion, the camera being found in the rubble afterwards. The red Vauxhall Cavalier carrying the bomb can be seen on the right side of the picture.

A judge has issued a ruling in the 1998 bombing in the Northern Ireland town of Omagh. Defendant Sean Hoey, who faced 56 charges relating to a car bomb that killed 29 people and injured more than 200, has been found not guilty. 

A stunned silence in the public gallery of Belfast Crown Court greeted the verdict in the worst bombing during three decades of so-called troubles in Northern Ireland. Electrician Sean Hoey, 38, was accused of being the principle bomb-maker in a group of conspirators. Only one other person was charged in the case and he is awaiting retrial after having his conviction overturned.

Hoey was said to have been among those who broke away from the Irish Republican Army months after the Good Friday Peace Agreement was negotiated.

In summing up, Judge Reginald Weir said he was critical of forensic evidence presented by the prosecution that relied heavily on a new kind of DNA testing. He also criticized the police for how they handled and stored the evidence, with possible cross-contamination.  The judge also singled out two police officers who he said had exaggerated in order to gain a conviction.

For families of the victims, it was a disappointment after waiting nearly a decade for justice. Lawrence Rush lost his wife in the blast. He was in the courthouse when the decision was announced.

"It is devastating," he said. "It is a disaster the way that this investigation was held, and I can say no more about it. All I know is that I am tired, you know, and I am exhausted. It has been a long corridor, 10 years of pain and hope.

"The legal system is here to protect human rights," said Victor Barker, who lost his son in the attack. "It is here to protect Sean Hoey's human rights. I am a lawyer, I believe in the system. Sometimes I find it hard to live with, but I must stand by it because that is the system of justice which ordinary decent people in this country live by. It is only a great shame that my son and the 29 people that died in Omagh had no human right at all."

Families of those killed are now calling for a full public inquiry into the bombing. It is also possible that a civil case may be pursued next year.