The 51-year-old will be moved from high-security Belmarsh prison in south-east London to the RAF (Royal Air Force) Northolt air base in west London where a military aircraft will be waiting to take off, heading for an isolated airstrip near the Jordanian capital of Amman.
The UK Home Office, meanwhile, has refused to either deny or confirm the report, saying: "Our focus is on seeing him on a plane to Jordan at the earliest opportunity."
His wife and five children are expected to remain in Britain.
Qatada had originally fled the Middle East and arrived in the UK in 1993, where he was granted asylum the following year.
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His increasingly radical sermons caught the attention of the security services in Britain and he was dubbed Osama bin Laden's right-hand man in Europe.
He now faces a retrial on those charges.
The extradition was finally made possible after the British and Jordanian governments finished ratifying a treaty which includes a series of legal agreements aimed at ensuring Qatada's right to a fair trial as per international law.
The treaty, which ensures that evidence obtained through torture will not be used at the retrial, was printed on Tuesday in the Jordanian government's official gazette.
The announcement paved the way for UK home secretary Theresa May to begin extradition proceedings.