The treaty is now awaiting approval by Jordan's King Abdullah, the final key stage before the deal becomes law.
The vote in parliament means the long-drawn process to deport the cleric from Britain is likely to resume within weeks.
53-year-old 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.
"The government has ratified the treaty as well as Parliament. The Treaty is mutual legal assistance and can include any persons from each country," Mohammad Al-Momani, Jordan's information minister, told the BBC.
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The treaty goes into law after the king issues a royal decree and the document is published in the Jordanian government's official gazette.
The UK-Jordan Treaty on Mutual Legal Assistance is before MPs and Lords at parliament in Westminster.
It is expected to become part of British law on June 21, unless there is an unexpected late request for a vote or debate in Parliament.
Assuming the treaty passes all of its legal hurdles in both countries, the cleric's deportation would then resume.
If he keeps to an assurance given in court that he will leave the UK following the treaty, he could be put on a plane to Amman in a matter of weeks.
"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.
He requested asylum on grounds of religious persecution, claiming he had been tortured in Jordan.
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.