The judges said his conditions could be treated in the U.S., and concluded that "there is nothing to suggest that extradition in this case would be unjust or oppressive."
Before Friday's ruling, a small group of Islamist protesters gathered outside the court to denounce the planned extraditions. A few scuffled briefly with police and one seized a placard reading "Sling His Hook" from a demonstrator expressing the opposite view.
While al-Masri has been portrayed in the British media as one of the most dangerous men in the country, the case of Babar Ahmad has raised concerns among legal experts and human rights advocates.
Ahmad, a London computer expert, is accused in the U.S. of running terrorist-funding websites. He and Ahsan both face charges including using a website to provide support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.
Ahmad and Ahsan could be in court in Connecticut, where an Internet service provider was allegedly used to host one of the websites, on Saturday if they are extradited as planned from Britain.
A hearing was scheduled for Ahmad and Ahsan in U.S. District Court in New Haven on Saturday morning, U.S. Marshal Joseph Faughnan said Friday.
Some lawyers and lawmakers have expressed concerns about the case, because Britain agreed to extradite him even though his alleged crimes were committed in Britain and British courts declined to prosecute him for lack of evidence.
In prison since 2004, Ahmad has been held without charge for the longest period of any British citizen detained since the Sept. 11 attacks.
In a statement read on his behalf outside court, Ahmad said his case had exposed flaws in U.S.-U.K. extradition arrangements. "I leave with my head held high, having won the moral victory," he said.
His father, Ashfaq Ahmad, said he would continue to fight for his son.
"It's not just one Babar Ahmad. Tomorrow there will be another Babar Ahmad and another one," he said.