Mrs May said the treaty, guaranteeing fair trials in Britain and Jordan, would take precedence over current Jordanian law.
The courts have rejected the home secretary’s attempts to deport Abu Qatada to his native Jordan because of concerns that evidence obtained by torture could be used against him.
The treaty is an attempt to reassure the courts that the preacher would have a fair trial in Jordan on terrorism charges.
Mrs May’s statement followed the appeal court’s refusal yesterday to refer the case to the supreme court.
She reacted by saying the government would apply directly to the supreme court for permission to appeal. She said the entire process would take “many months”, during which she believed Abu Qatada should remain “behind bars”.
Abu Qatada, once described by a Spanish judge as “the spiritual leader of the mujahedeen in Europe”, has been resident in the UK since 1993 and was returned to jail last month after being arrested for alleged bail breaches.
Last month, the appeal court backed an earlier ruling that Qatada, also known as Omar Othman, could not be deported to Jordan over fears that evidence obtained through torture would be used against him.
This is despite assurances from Jordan, where he was convicted in his absence of terrorism charges in 1999, that this type of evidence would not be used.
Qatada, who featured in hate sermons found on videos in the flat of one of the 11 September bombers, has thwarted every attempt by the government to deport him.
In December 2001, following the 11 September attacks in the US, he became one of Britain’s most wanted men after going on the run from his home.
The following year, he was arrested in the capital and detained in Belmarsh high-security jail.
Labour, which wants Qatada deported and tried in Jordan, argues that the government’s legal strategy has failed.