Last week, Jordan's parliament ratified the Treaty on Mutual Legal Assistance, intended to ease human rights concerns preventing the deportation of the cleric, whose real name is Omar Mahmoud Mohammed Othman, from Britain to Jordan.
Abdullah's endorsement came in a royal decree published in Jordanian newspapers Tuesday.
Since 2001, successive British governments tried to deport Abu Qatada, but courts there blocked extradition over concerns that evidence obtained under torture could be used against him.
Recently, Abu Qatada said he'd go to Jordan voluntarily if the treaty is ratified.
He is wanted in Jordan for retrial in several terror cases in which he was sentenced in absentia.