But lawyers for Babar Ahmad said he was being made a scapegoat and vowed to fight his extradition in the High Court.
"This is a difficult and troubling case," Judge Timothy Workman said on Tuesday, allowing the extradition after receiving assurance from US authorities that they would not seek the death penalty or declare Ahmad an "enemy combatant".
Ahmad, 31, has been in British custody since his arrest last August on a US extradition warrant that accuses him of supporting terrorism, conspiring to kill Americans and running Web sites used to fund terrorists.
British Home Secretary Charles Clarke has 60 days to decide whether Ahmad will be extradited.
Fight to the end
Ahmad's lawyers and relatives said they would challenge the extradition.
"We are still hopeful he will not be extradited," Ahmad's father Ashfaq Ahmad said. "The home secretary - let's see what he decides. Even if he decides Babar should be extradited, we will go to a higher court and we will fight it to the very end."
Ahmad, who was indicted in the US in October, is accused of running several websites, including Azzam.com, which investigators say was used to recruit members for al-Qaida, the Taliban and Chechen separatists.
Ahmad's lawyers had argued that he could be tried by a military tribunal and face the death penalty if convicted. British law forbids the extradition of suspects who could face capital punishment.