The man said to be the leader of the dissident republican group, the Real IRA, has been found guilty of directing terrorism and membership of an illegal organisation.
Michael McKevitt denied all the charges
The verdict against Michael McKevitt, 53, from Blackrock in County Louth was delivered at the Special Criminal Court in Dublin on Wednesday.
It is the first time the charge of directing terrorism has been brought before a court in the Irish Republic.
The offence was one of a range of measures introduced by the Irish Government in the wake of the Omagh bombing.
Twenty-nine men, women and children died and hundreds were injured when the Real IRA detonated a car bomb in the County Tyrone town on 15 August 1998.
However, the judges stressed that the offences McKevitt was convicted of dated from after the atrocity.
The County Louth businessman had denied the charges.
McKevitt was not in court when the verdict was delivered by the court's three judges.
He refused to come into the court.
In their judgement, the three justices said the chief prosecution witness, FBI agent David Rupert, was a truthful witness and his credibility had not been impugned.
Sentencing is expected at the same court on Thursday.
McKevitt has indicated that he would be appealing against the convictions.
A statement on his behalf was read out by his wife Bernadette Sands McKevitt.
McKevitt said he had protested in the belief he was "denied the right to a fair trial".
"I believe my opinion is supported by a plethora of irrefutable facts", the statement added.
Detective Chief Garda Superintendent Martin Callinan said the verdict was a "significant result".
"It was a particularly long process in that we had a number of court appearances and very difficult complex security issues," he said.
Mr Callinan said that FBI agent Mr Rupert had been a key witness and praised his contributions to the proceedings.
"The decision today has vindicated his position and we are very very grateful to him for having come forward," he said.
"It was a very brave thing to do."
Michael Gallagher welcomed the verdict
Some of the Omagh relatives were in the court for the verdict.
Laurence Rush, whose wife was killed in the Omagh bombing, welcomed the verdict.
"I feel very happy at what has happened and we are now waiting for the sentence," he said.
Michael Gallagher, whose 21-year-old son Aidan was killed in the blast said he was "absolutely delighted" the verdict had gone the way it had.
The trial came to a speedy end last month after Mr McKevitt sacked his legal team, denouncing the proceedings as a "political show trial".
The following day he refused to come into the courtroom, saying he wished to
take no further part in the trial.
The Real IRA was formed after a split within the mainstream IRA. The dissident group is opposed to the Northern Ireland peace process.