The agreement, unveiled by Home Secretary Theresa May in April, aims to allay fears that evidence extracted through torture will be used against the terror suspect at a retrial.
Last month, Qatada unexpectedly volunteered to leave the country as soon as the treaty between the UK and Jordan is ratified by both countries.
The agreement has been approved by both houses of the Jordanian parliament, but must still be signed off by the country’s King Abdullah. The UK government expects the treaty to be ratified in Britain by 21 June.
A Home Office spokesman said: “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.”
The government has been trying to deport Qatada to Jordan, where he was convicted of terror charges in his absence in 1999, for eight years.
In a bid to address concerns raised by immigration judges about the use of torture in Jordan, Mrs May revealed that a new agreement had been drawn up with the country. But the Home Secretary warned that, even when the treaty is fully ratified, it will not necessarily mean that Qatada will be on a plane to Jordan within days. The case remains open to appeal.
Qatada is currently behind bars in London’s Belmarsh Prison after breaching a bail condition which restricts use of mobile phones and other communication devices.