Radical Muslim cleric Abu Hamza can be extradited to the US after Europe's human rights judges rejected his request for an appeal, officials have said.
Hamza wanted to fight a European Court of Human Rights ruling that extradition would not breach his human rights.
But his request was rejected by a panel of judges, a spokesman for the court said.
The unanimous judgment said there would be no human rights breach either as a result of likely detention in ADX Florence "supermax" prison in Colorado, or the length of possible sentences on conviction.
The decision means Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, can now be extradited with four others, including terror suspect Babar Ahmad.
Computer expert Ahmad has been held in a UK prison without trial for eight years after being accused of raising funds for terrorism.
The request for an appeal delayed a total of five cases related to the same judgment. The other cases involve Seyla Talha Ahsan, Adel Abdul Bary and Khaled al Fawwaz.
The five are likely to be put on a plane to the US within two or three weeks, it is understood.
A Home Office spokesman said: "The Home Secretary welcomes today's decision not to refer the cases of Abu Hamza and four others to the Grand Chamber.
"This follows the judgment of the European Court of Human Rights on April 10 to allow the extradition of these five terrorism suspects to the US.
"We will work to ensure that the individuals are handed over to the US authorities as quickly as possible."
The judges said that between 1999 and 2006 the men were indicted on various terrorism charges in America.
Hamza has been charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001 and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.
Bary and Al Fawwaz were indicted - with al Qaeda leader Osama bin Laden and 20 others - for their alleged involvement in, or support for, the bombing of US embassies in Nairobi, Kenya, and Dar es Salaam, Tanzania, in 1998. Al Fawwaz faces more than 269 counts of murder.
Ahmad and Ahsan are accused of offences including providing support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.