Judge Reginald Weir, who heard the case without a jury at Belfast Crown Court, said the prosecution evidence fell short of the standard needed to convict Hoey.
Prosecution and defence lawyers had wrangled over whether DNA evidence was reliable enough for a conviction during the 56-day trial.
Hoey was also cleared of a series of other charges linked to bombings and murders on police and military installations across British-run Northern Ireland before the Omagh attack.
Two hundred people were wounded in the Omagh bombing, which was carried out by the Real Irish Republican Army, an offshoot of the Irish Republican Army (IRA).
The dissident Catholic group was opposed to a 1997 ceasefire by the IRA in its campaign to force Britain to leave Northern Ireland.
The peace process was aimed at ending decades of sectarian violence between nationalist Catholics and unionist Protestants in the province.
Hoey was accused of engineering the 225kg car bomb that ripped through the County Tyrone market town.
A telephone call received by the authorities before the bombing said that explosives were on Omagh’s main street, but no precise information was given on the bomb’s location during the warning.
During the evacuation from the street, police officers unwittingly herded people towards the bomb before it detonated.
The only individual jailed for the Omagh bombing, Colm Murphy from the Irish Republic, had his conviction quashed by a Dublin court in 2005 but faces a retrial.