Ahmad, 31, a computer expert from London, is accused of running U.S.-based Web sites supporting terrorism and encouraging Muslims to wage holy war.
The case will now be referred to Home Secretary Charles Clarke for final approval and Ahmad has the right to appeal the decision to the High Court.
The U.S. government wants Ahmad on charges of "conspiring to support terrorism" dating back to 1997, saying he "sought, invited and solicited contributions" via Web sites and emails.
It claims his Web sites urged Muslims to use "every means at their disposal" to train for jihad, or holy war.
The Web sites allegedly called for support for terrorist causes in Afghanistan and Chechnya, and encouraged the transfer of money and equipment via the sites.
Lawyers for Ahmad said if sent to the United States, he could be at risk of the death penalty or being imprisoned in Guantanamo Bay.
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