The deal between the two countries, finalised in August, is expected to be used to extradite to Amman London-based Muslim cleric Abu Qatada as part of a crackdown on Islamists after the 7 July London bomb attacks.
The agreement to appoint the Jordanian rights group Adalah (justice in Arabic) to monitor the deal was announced during a meeting between Jordanian Interior Minister Awni Yervas and Foreign Office Minister of State Kim Howells on Monday.
Yervas and Howells "announced the agreement with an independent Jordanian human rights organisation that will play the role of the monitoring body as stipulated in the (accord) on deportations", a British embassy statement said.
"Jordan, in this sense, is a pioneering case because here we have identified what we think will be a very good, very independent, monitoring body," Howells said in the statement.
Days after Jordan and Britain signed the extradition agreement in August, Human Rights Watch warned that London would be breaking international law if it deports Abu Qatada to Amman where he could face "a serious risk of torture".
UK Foreign Office Minister Kim
Howells (R) announced the deal
"There is still torture in Jordan, especially with regard to security suspects," Joe Stork, deputy director of Human Rights Watch's Middle East division, said in a statement at the time.
Legal sources in Jordan have said the authorities will charge Abu Qatada with plotting to stage terrorist attacks when he is extradited from Britain - a crime which carries a sentence of up to 15 years in prison.
Abu Qatada - also known as also known as Omar Abu Omar - was arrested in Britain along with nine other foreigners in a crackdown on Islamists after the deadly 7 July bomb attacks that killed 52 people plus four bombers in London.
Born under the name Omar Mahmud Mohammed Othman, the Jordanian cleric has been labelled al-Qaida's "European spiritual leader".
Tapes of his sermons were found at a flat in Hamburg, Germany, used by some of the 11 September 2001 hijackers who flew planes into the World Trade Centre in New York and the Pentagon in Washington.
A date for his extradition has not been announced, and Howells told the state-run Petra news agency the arrangement should be worked out within a year.