Abu Qatada is expected to arrive in Jordan by Sunday, the AFP news agency has reported.
The legal treaty between the UK and Jordan ensuring that the radical cleric would receive a fair trial was fully ratified on Tuesday, preparing the way for his deportation.
Qatada unexpectedly volunteered to leave the country as soon as the treaty is ratified by both countries in May.
His deportation will make the end of a legal battle which has been bruising both for the taxpayer's pocket and personally for Theresa May.
The Government has been trying to deport Qatada to Jordan, where he was convicted of terror charges in his absence in 1999, for about eight years.
It is estimated just the legal fees to try and remove him have cost the taxpayer more than £1.7 million since 2005.
Qatada is currently behind bars in London's Belmarsh prison after breaching a bail condition which restricts use of mobile phones and other communication devices.
The Special Immigration Appeals Commission (Siac) previously heard that a USB stick understood to belong to Qatada's eldest son contained ''jihadist files'' made by the ''media wing of al Qaida''.
The terror suspect is also being investigated by Scotland Yard over suspected extremist material found during the search of his home.
More to follow..