Britain is to extradite Abu Hamza al-Masri to the United States as soon as possible, after he failed in a last-ditch legal attempt to avoid deportation.
Washington accuses the suspected terrorist and four others of supporting al Qaeda, aiding a kidnapping in Yemen and plotting to open a US training camp.
Abu Hamza, 54, a one-eyed preacher from Egypt, achieved notoriety for praising the September 11 attacks on the United States.
High Court judges in London ruled on Friday that he and Babar Ahmad, Syed Talha Ahsan, Adel Abdul Bary and Khaled al-Fawwaz failed to show "new and compelling" reasons not to send them.
The appeal came after the European Court of Human Rights backed successive UK courts in ruling for extradition.
Judges said their extradition "may proceed immediately".
Judges Sir John Thomas and Mr Justice Ousley said there were be no further appeals.
"It is not just to anyone that proceedings such as these should last between 14 and eight years," they said.