Judges at the European Court of Human Rights in Strasbourg ruled that Hamza, who became the face of violent extremism in Britain, must go back to the US.
Four other terror suspects, who are wanted in the US on various charges, will also be extradited.
The judges rejected claims that the five men would be subjected to “ill-treatment” if they were forced to go to the US.
The men complained that prison conditions and jail terms would mean “torture or inhuman or degrading treatment or punishment”, which would breach the European code of human rights.
The court halted extradition proceedings in 2010, arguing that it needed to consider complaints that the rights of the men would be breeched if they were exposed to life imprisonment without parole and solitary confinement.
The court called for further submissions in the case of a sixth man, Haroon Rashid Aswat, who has mental health issues.
Prime Minister David Cameron said: “I am very pleased with the news.
“It is quite right that we have proper legal processes, although sometimes one can get frustrated with how long they take.
“I think it is very important that the deportation and expulsion arrangements (work) promptly and properly, particularly when people are accused of very serious crimes.”