Home Secretary Theresa May has been given the go-ahead for the immediate extradition of radical cleric Abu Hamza to the United States.
Two High Court judges in London also rejected last-ditch challenges by four other terror suspects against removal from the United Kingdom.
Dismissing their actions in a ruling lasting more than two hours, Sir John Thomas, president of the Queen's Bench Division, announced their "extradition to the United States of America may proceed immediately".
Sir John and Mr Justice Ouseley "released" Mrs May from undertakings she had given pending Friday's judgment not to extradite.
After the decisions were given, a Home Office spokesman said: "We welcome the High Court decision on Abu Hamza and others. We are now working to extradite these men as quickly as possible."
The judges rejected an application by 54-year-old Hamza, a former imam at Finsbury Park mosque in north London, to be given time to undergo a brain scan his lawyers said could show he is medically unfit to face trial.
They also threw out challenges by Babar Ahmad, Syed Ahsan, Khaled Al-Fawwaz and Adel Abdul Bary. All five cases returned to the High Court after judges at the European Court of Human Rights (ECHR) refused to intervene and stop the Home Secretary extraditing them.
Welcoming the decision, a US Embassy spokeswoman said: "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."
Between 1999 and 2006, the men were indicted on various terrorism charges in America. Hamza, who was jailed in the UK for seven years for soliciting to murder and inciting racial hatred in 2006, first faced an extradition request from the Americans in 2004.
He 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.