"This decision constitutes above all a moral victory for the state of Israel and for victims of terrorism," Lieberman said.
It "confirms the opinion of those who know what happened in the early 2000s but which many in the world refused to recognise because of hypocrisy, known vested interests or anti-Semitism," he said.
"Terrorism is an integral part of the very structure of the Palestinian Authority," Lieberman charged.
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A jury in New York ordered Palestinian authorities to pay the damages to American victims of six separate attacks in Israel between 2002 and 2004.
It found the Palestinian Authority and the Palestine Liberation Organisation liable on 25 separate charges and awarded the damages after one day of deliberations.
Eleven plaintiff families filed suit in federal court against both the PA and the PLO following the attacks that killed 33 people and injured more than 390.
The plaintiffs had pressed for the PA and the PLO to be held accountable for supporting the attacks by members of the Islamist movement Hamas and the Al-Aqsa Martyrs' Brigade, linked to the mainstream Fatah faction.
But lawyers for the PA said it should not be held responsible for "crazy and terrible" attacks committed in Israel, insisting the assailants had acted independently.