Morgan also found the Real IRA, who masterminded the bombing and are a dissident offshoot of the Irish Republican Army, liable for the attack.
"Those involved in the planning, preparation, planting and detonation of the bomb recognised the likelihood of serious injury or death from its detonation but decided to take that risk," he said.
It is the first time anywhere in the world that members of a fighter organisation have been sued and the judgement could pave the way for victims of violence to sue other such groups.
Speaking to Al Jazeera, Jason McCue, a lawyer representing the families, said: "The families are over the moon. We will now look at the enforcement of the ruling.
"It [the ruling] sets a big precedent. They [the families] have shown that you can find justice, that you can pursue such cases yourself and that the terrorists can't get away with it."
Stanley McCombe, whose wife died in the attack, said it was "a result we hoped for but didn't expect".
"We didn't build our hopes up because we've been let down so many times before," he said.
But he added: "It was never about money. We can stand and say that these guys are responsible for Omagh, that's what we wanted."
Michael Gallagher, whose son Aidan was killed in the bombing, said: "Eight years has just come to an end all of a sudden. It is a result better than we could ever have imagined."
"We have sent out an important message to terrorists and their victims around the world; you now have a way of challenging those who've murdered your loved ones.
"I think it is a tremendous moral victory for the families."
The Real IRA exploded the car bomb in the market town on August 15, 1998, but despite extensive police investigations, no one has ever been convicted in a criminal court of causing the deaths.
The court heard from spouses, parents, brothers and sisters of the victims, as well as police officers who described the scenes of carnage they encountered at the scene of the bombing.
Daniel Brennan, the lead lawyer for the case, had said that the judgement could open the floodgates for similar actions against fighters responsible for the bulk of the 3,700 deaths in Northern Ireland's four-decade conflict.
"Regardless of the result this has been worthwhile, it has empowered the families like never before," he said.
Bill Clinton, the former US president, who visited Omagh while in power, has been among the backers of the legal action, which has taken eight years to reach a verdict.
The families' civil case has cost an estimated $3.17m.