Hamza had applied along with four others to reopen their case, but the Starsbourg-based Grand Chamber said "Today the Grand Chamber Panel decided to reject the request", without giving reasons.
There is no legal impediment against their extradition now, official courses said.
"The Home Secretary welcomes today's decision not to refer the cases of Abu Hamza and four others to the Grand Chamber. This follows the judgement of the European Court of Human Rights on April 10 to allow the extradition of these five terrorism suspects to the US," a Home Office spokesman said.
"We will work to ensure that the individuals are handed over to the US authorities as quickly as possible," he added.
Besides Hamza, the other four are Babar Ahmad, Talha Ahsan, Adel Abdul Bary and Khaled-al-Fawwaz.
In a statement, the Strasbourg court said: "On 10 April 2012 the European Court of Human Rights held, in the case of Babar Ahmad and Others v. The United Kingdom, that there would be no violation of the applicants' rights if extradited to stand trial in the United States".
"On 9/10 July 2012, five of the applicants lodged a request for referral of the case to the Grand Chamber. Today the Grand Chamber Panel decided to reject the request. This means that the Chamber judgement of 10 April 2012 is now final," it added.