The Home Office has confirmed it is now preparing to have Qatada sent home to face trial for terrorism offences after years of fighting for his deportation.
Qatada, once described by a judge as Osama bin Laden's right-hand man in Europe, was arrested by officers from the UK Border Agency at his home in London.
He has been informed the intention is to deport him to Jordan on or around April 30.
A Home Office spokesman said: "UK Border Agency officers have today arrested Abu Qatada and told him that we intend to resume deportation proceedings against him."
Sky's deputy political editor Joey Jones said the move must mean the government is confident it has the assurances it requires from Jordan about his future trial.
The European Court of Human Rights (ECHR) ruled in January that the cleric could not be sent back without promises evidence gained through torture would not be used.
The government has until midnight tonight to appeal but has instead focused its efforts on securing the necessary agreement from the Jordanian authorities.
Keith Vaz, the chairman of the Commons Home Affairs Select Committee, says the Jordanian officials have given the government "all the assurances it needs" to deport Qatada.
Ms May has to show she has made progress in the case by the start of next month or judges could have lifted 51-year-old Qatada's stringent bail conditions.
The Home Secretary is due to deliver an emergency statement to the House of Commons at 3.30pm to update MPs on the developments.
Qatada - who has been on bail from Long Lartin high-security jail in February under stringent conditions - is likely to launch a new legal challenge against deportation.
His legal team are due to apply for bail at a hearing at the Special Immigration Appeals Commission in central London later today, according to the Judicial Communications office.
Labour had earlier accused the government of allowing "too much drift and delay".
Shadow home secretary Yvette Cooper argued that Ms May should have acted sooner to prevent the cleric's release from prison in the first place and declared she needed to get "an urgent grip of this case".
She said: "The Home Secretary needs to explain urgently to Parliament what she is doing to get Abu Qatada deported and to make sure there are strong enough safeguards to protect public safety in the meantime."
Last week, the Home Office denied it had reached any deal with the Jordanian government. Jordan has previously said Qatada would get a fair trial.
Qatada, who is also known as Omar Othman, was convicted in his absence in Jordan of involvement with terror attacks in 1998 and has featured in hate sermons found on videos in the flat of one of the September 11 bombers.
He has been held for six-and-half-years, more than any other detainee in modern immigration history, and thwarted every attempt by the government so far to deport him.
The cleric, who is considered a threat to the UK's national security, was released in February on some of the toughest bail conditions imposed since the September 11 attacks.
He can leave his London home for two one-hour periods each day, is banned from taking his youngest child to school and cannot talk to anyone who has not been vetted by the security services.
He is also banned from visiting mosques, leading prayers, giving lectures of preaching other than to offer advice to his wife and children at home.