Five suspected terrorists including Abu Hamza al-Masri can be extradited to the US, ending a long legal battle, UK High Court judges have ruled.
The radical cleric, Babar Ahmad, Syed Talha Ahsan, Adel Abdul Bary and Khaled al-Fawwaz failed to show "new and compelling" reasons not to send them.
Their appeal came after the European Court of Human Rights backed successive UK courts in ruling for extradition.
Judges said their extradition "may proceed immediately".
A Home Office spokesman, meanwhile, welcomed the decision and said it was "working to extradite these men as quickly as possible".
The BBC understands two US civilian jets - one of which is registered to the US Department of Justice - are on the tarmac at an air base in eastern England.
Judges Sir John Thomas and Mr Justice Ousley said in their ruling that there was an "overwhelming public interest in the functioning of the extradition system" and that there was "no appeal from our decision".
Of the long legal battle to extradite the men, Sir John told the court: "It is unacceptable that extradition proceedings should take more than a relatively short time, to be measured in months not years.
"It is not just to anyone that proceedings such as these should last between 14 and eight years."
There was no doubt each man had, over the years, "either taken or had the opportunity to take every conceivable point to prevent his extradition to the United States", he added.
The written ruling, read out in court, concluded that "each of the claimants' applications for permission to apply for judicial review or for a re-opening of the statutory appeals be dismissed".
The judges rejected a plea by Abu Hamza to delay his extradition so he could undergo an MRI brain scan which, his lawyers said, could show he was unfit to plead because of degenerative problems.
"The sooner he is put on trial the better," they said.
The 54-year-old, a former imam at Finsbury Park mosque, north London, was suffering from chronic sleep deprivation and depression as a result of eight years in prison, his lawyers added.
The BBC's Dominic Casciani, at the High Court, said the British government had got the result it had wanted to see for years on Abu Hamza, who the US first attempted to extradite in 2004.
His extradition was halted when the UK decided to try him on allegations relating to his sermons. He was convicted in 2006.
The judges also rejected appeals from Mr al-Fawwaz and Mr Bary, who are accused of being aides to Osama Bin Laden in London.
The US alleges they promoted violent jihad against the West and were involved in the 1998 US embassy bombings in East Africa, which killed more than 200 people.
The battle to stay in the UK is also over for Babar Ahmad and Talha Ahsan, who are accused of running pro-jihad website Azzam.com - which the US says was hosted there - and of helping terrorists.
Mr Ahmad's father, Ashfaq, said outside court he was appalled the British legal system had let him down "in a manner more befitting of a Third World country than one of the world's oldest democracies".
"We will never abandon our struggle for justice for Babar and the truth will eventually emerge of what will be forever remembered as a shameful chapter in the history of Britain," he added.
And Emma Norton, legal officer for human rights group Liberty, said that, as Mr Ahmad's alleged offences took place in the UK, "It beggars belief that he won't be tried here."
"Isn't British justice - so admired around the world - capable of dealing with crimes committed in the UK by its own citizens?" she added.
In a statement released by its embassy in London, the US said it was "pleased" the men were being extradited after "a lengthy process of litigation".
"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," it added.