The High Court ruling cleared the way for Hamza and four other terrorism suspects to be extradited immediately, the BBC reported.
"There is a need for finality. There is no appeal from our decision," court said. "There is an overwhelming public interest in the functioning of the extradition system."
In the United States, Hamza is accused of planning to establish a terrorist training camp in Oregon and of assisting in taking hostages in Yemen.
Britain's Home Office welcomed the decision, the BBC said.
"We are now working to extradite these men as quickly as possible," a spokesman said.
Hamza, Babar Ahmad, Syed Talha Ahsan, Khaled al-Fawwaz and Adel Abdul Bary collectively fought against extradition for more than eight years, involving appeals in both British courts and the European Court of Human Rights.
Hamza, 54, held for seven years for soliciting murder and inciting racial hatred, has been fighting extradition since 2004. His lawyers oppose extradition on grounds he suffers from memory loss and depression, and is unfit to plead.
The court said it was unconvinced Hamza was unfit to stand trial.
Ahmad, 37, and Ahsan, 33, are accused of raising funds for terrorism through a website. Fawwaz allegedly was an aide to Osama bin Laden during the 1990s and Bary also reportedly worked closely with the founder of al-Qaida.
In a statement prepared before the verdict, Ahmad thank his family and supporters.
"By exposing the fallacy of [Britain's] extradition arrangements with the U.S., I leave with my head held high having won the moral victory," he said.