The decision means that the extradition of the men, wanted for years by the US, is likely to happen within weeks.
The Home Office welcomed the decision, saying it would ensure the extraditions happen as quickly as possible.
Each man had said they would face inhumane treatment in the United States if they were sent there.
Abu Hamza is accused of planning a terror training camp in the US and assisting hostage-taking in Yemen.
Adel Abdul Bary, Khaled Al Fawwaz are accused of being aides to Osama bin Laden in London.
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.