Abu Hamza and four other terror suspects are believed to be on their way to the United States after losing a last-ditch court appeal at the High Court to avoid extradition.
A cavalcade of police vehicles, including armoured vans, arrived at HMP Long Lartin in Worcestershire at around 6.30pm on Friday evening.
After about an hour, the vehicles, understood to have Hamza and the other men inside, left the prison grounds.
Under heavy security, they drove off at speed, thought to have been en route to an airport in the south of the UK where the men would be put on to military aircraft and flown to America.
Hamza, along with Babar Ahmad, Khaled Al-Fawwaz, Syed Ahsan and Adel Abdul Bary, cannot appeal Friday's decision. It is the final ruling in the suspects' legal battle which has collectively spanned more than eight years.
A Home Office spokesman said: "We welcome the High Court decision on Abu Hamza and others."
Dozens of protesters gathered outside the High Court before the decision in support of Syed Ahsan and Babar Ahmad.
Ahmad, a computer expert from south London, and Ahsan are accused of offences including using a website to provide support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.
They wanted their removal stopped so that they could challenge a decision by the Director of Public Prosecutions not to allow British businessman Karl Watkin, a campaigner against the UK's extradition arrangements with the United States, to bring private prosecutions against them in the UK.
After the ruling, Babar Ahmad's father, Ashfaq Ahmad, stood on the steps of the High Court and said:
"The truth will eventually emerge of what will be forever remembered as a shameful chapter in the history of Britain.
"After over 40 years of paying taxes in this country, I am appalled that the system has let me down in a manner more befitting of a third world country than one of the world's oldest democracies."
A statement prepared by Babar Ahmad in prison before the verdict, read out by one of his supporters, said: "By exposing the fallacy of the UK's extradition arrangements with the US, I leave with my head held high having won the moral victory."
Emma Norton, legal officer for human rights group Liberty, said: "Mr Ahmad's alleged offences happened in this country - it beggars belief that he won't be tried here.
"This is yet another example of the dangers of our flawed extradition arrangements. Isn't British justice - so admired around the world - capable of dealing with crimes committed in the UK by its own citizens?"
A statement from Karl Watkin said: “I am extremely frustrated (but not at all surprised) by the Judges’ decision regarding Babar Ahmad. I have no regrets over pursuing a private prosecution – it was the right thing to do.
“No matter how much the public and their representative MPs protest at today’s outrage, no British court will ever try these two suspects.
RIP British justice.”
Welcoming the decision, a US Embassy spokeswoman said: "These extraditions mark the end of a lengthy process of litigation through the UK courts and the ECHR.
"The US government agrees with the ECHR's findings that the conditions of confinement in US prisons - including in maximum security facilities - do not violate European standards.
"In fact, the court found that services and activities provided in US prisons surpass what is available in most European prisons.
"The law enforcement relationship between the United States and United Kingdom is predicated on trust, respect, and the common goals of protecting our nations and eliminating safe havens for criminals, including terrorists."
The judges rejected a plea by 54-year-old Hamza that the former imam should be given time to undergo a brain scan to see whether he was medically fit to face trial.
His QC, Alun Jones, said the Egyptian-born preacher, who lost both hands and an eye fighting the Soviet Union in Afghanistan, was suffering from depression, lack of concentration and failing memory.
This was probably linked to the chronic sleep deprivation he had endured while held at top-security Belmarsh prison in south-east London for more than eight years in "utterly unacceptable conditions", it was claimed.
His cell lights had been switched on every hour of the night to make sure he was moving, said Mr Jones.
Hamza suffered from diabetes, raised blood pressure and excessive sweating which required him to shower twice a day.
He also suffered from repeated infections to the stumps of his forearms.
During the Hamza hearing, judge Sir John Thomas himself observed: "There are excellent medical facilities in the United States.
"The sooner he (Hamza) stands trial the better. If he is at risk of a degenerative condition, the sooner he is put on trial the better. I don't see how delay is in the interests of justice."
Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred in 2006, first faced an extradition request from the Americans in 2004.
Bary and Al-Fawwaz were indicted - with Osama bin Laden and 20 others - for their alleged involvement in, or support for, the bombing of US embassies in Nairobi and Dar es Salaam in 1998. Al-Fawwaz faces more than 269 counts of murder.
The five suspects will now be immediately extradited to the United States.
Dismissing the five cases, Sir John announced:
"There is an overwhelming public interest in the proper functioning of the extradition arrangements and the honouring of extradition treaties.
"It is also in the interest of justice that those accused of very serious crimes, as each of these claimants is in these proceedings, are tried as quickly as possible as is consistent with the interests of justice."