Awni Yirfas, the minister, told state television on Friday night that Britain had verbally informed authorities in Amman that the cleric "will be sent back to Jordan next week".
Abu Qatada would be "retried under a Jordanian law which allows persons convicted and sentenced in absentia the right to retrial once captured," Yirfas said.
The countries signed an extradition agreement earlier this week.
Omar Mahmood Othman Abu Omar, better known as Abu Qatada, was among 10 foreigners that British police arrested on Thursday on suspicion of posing a threat to national security in Britain.
The detentions came days after British Prime Minister Tony Blair announced tough new proposals to deport Muslim extremists in the wake of the 7 July bombings in London that killed 56 people.
Born in the West Bank town of Bethlehem in 1960, Abu Qatada was convicted in absentia in Jordan in 2000 on charges of conspiring to attack US and Israeli tourists during the kingdom's millennium celebrations. According to the indictment, his role was primarily to finance the terror group.
The State Security Court sentenced him to 15 years in jail. In its judgment, the court said it had no evidence that Abu Qatada's group had links to the al-Qaida network led by Osama bin Laden.
The British police arrested Abu
Qatada on Thursday
But a Spanish judge has described Abu Qatada as Bin Laden's "spiritual ambassador in Europe".
The British authorities believe Abu Qatada inspired Mohamed Atta, the lead hijacker in the 11 September 2001 attacks on the United States.
The British government said 18 videotapes of Abu Qatada's sermons were found in a Hamburg flat used by Atta and two other hijackers.
At the end of another trial in 1998, a Jordanian military court found Abu Qatada and eight other militants guilty of conspiring to carry out acts of terror by detonating bombs outside an Amman hotel, a school, and under the cars of a former intelligence chief and a former interior minister.
In that case, Abu Qatada was sentenced in absentia to 15 years in jail.