The UK government has repeatedly tried to deport Qatada, who is wanted in his home country on terrorism charges since 1999.
But the courts so far have upheld his right to stay in Britain over fears that evidence obtained by torture may be used against him in the Middle Eastern country.
Representing the London-based cleric at a bail application hearing, Edward Fitzgerald has now said the terror suspect will return to Jordan once the treaty, unveiled last month by UK Home Secretary Theresa May, is ratified by the UK and Jordanian parliaments.
The treaty with the Jordanians, which is designed to ensure he will face a fair trial on terror charges without the use of evidence obtained by torture, was signed on March 24.
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Abu Qatada has been detained in a maximum-security prison in Britain for a total of seven years and five months while his deportation saga has continued.
Today's hearing has been adjourned until May 20, which means he will remain at Belmarsh Prison in south-east London till then.
The UK government lost an appeal against the ruling recently and also failed in its bid to get the case referred to the Supreme Court.
The Home Secretary said she was subsequently applying directly to the Supreme Court for permission to challenge the ruling.
Meanwhile, Robin Tam, appearing in court for the Home Secretary, said the treaty between Britain and Jordan would be laid before the Jordanian Parliament within the next few weeks, and the UK side of the process should be finished by late June.