King Abdullah's nod paves the way for the treaty to become law as soon as the document is published in the Jordanian government's official gazette.
In the UK, the treaty is expected to be passed by MPs and become law on Friday.
Qatada, currently in a London jail, has already indicated he will not challenge deportation if the treaty is passed because the document guarantees him a fair trial.
Jordan's Parliament had approved the treaty in two stages earlier this month, as it passed through the lower and upper house.
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The UK-Jordan Treaty on Mutual Legal Assistance is before MPs and Lords at Westminster.
Assuming the treaty passes all of its legal hurdles, the cleric's deportation would then resume.
UK Home Secretary Theresa May would be able to issue a fresh deportation order and the cleric would have time to respond if he wished to but that is expected to be only a few days.
"The government remains committed to securing Qatada's deportation as quickly as possible. We are pleased the Jordanian parliament has approved the treaty and we await its full ratification by the Jordanian government and the completion of ratification procedures in the UK," a Home Office spokesperson said.
Abu Qatada, wanted in Jordan on alleged terror charges, has fought against his deportation from the UK for almost eight years on the grounds that evidence obtained by torture may be used against him in his home country.