The radical Islamist preacher, who is in his early 50s, was driven out of the high-security Long Lartin prison in central England in a black van at high speed, television pictures showed.
Abu Qatada was expected to be taken to his home in northwest London where he will be under a curfew 16 hours a day but can leave his home between 8am and 4pm.
He will have to wear an electronic tag and who he meets will be restricted.
The heavily bearded Jordanian of Palestinian origin has been in jail in Britain for the past seven years fighting extradition, and also spent much of the time between 2002 and 2005 in detention or under house arrest.
Abu Qatada was convicted in absentia in Jordan in 1998 for involvement in terror attacks.
The decision by senior judges on Monday to uphold his appeal against extradition to Jordan was a major blow for the British government, which has fought for seven years to deport him.
Deputy Prime Minister Nick Clegg said on Tuesday that the government was determined to deport Abu Qatada.
“We strongly disagree with the court ruling. We are going to challenge it, we are going to take it to appeal,” Clegg told ITV television.
“We are absolutely determined to see this man get on a plane and go back to Jordan, he does not belong here,” Clegg said.
Home Secretary Theresa May has said had ordered Abu Qatada’s extradition after she was given assurances by Jordan that no evidence gained through the torture of two other men would be used against him in a retrial.
But the Special Immigration Appeals Commission – a semi-secret panel of British judges that deals with decisions on national security – said that could not be guaranteed.