The extradition was granted by UK home secretary John Reid and is the second to last stage before Gary McKinnon has to pack his bags. He has 14 days to appeal against Reid's order.
McKinnon told the Beeb he was "very worried" and feeling very let down by the government.
The US claims that McKinnon caused more than £375,235 worth of damage while poking around the computer networks at various US military institutions.
It says that one attack at the Earle Naval Weapons Station took place soon after 11 September 2001 and made it impossible to use critical systems.
One of the defence teams concerns is that he will be sent to Guantanamo Bay as a terrorist suspect and never be seen again.
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