Lauri Love, 31, who has Asperger's syndrome, is accused of hacking into the FBI, the US central bank and the country's missile defence agency.
Mr Love, from Stradishall, Suffolk, has previously said he feared he would die in a US prison if he was extradited.
A judge at Westminster Magistrates' Court made the extradition ruling.
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Earlier, his lawyer said his alleged hacking had "embarrassed" US authorities.
Tor Ekeland said the US government "had very, very bad security and these hacks utilised exploits that were publicly-known for months".
Mr Love's lawyers said he could face up to 99 years in prison if convicted of the hacking offences.
Earlier he stood in the dock as district judge Nina Tempia ruled he could be extradited to the US, where he could face trials in three different states.
He was first arrested at home in Suffolk in 2013 and had computer equipment seized by British police, who then released him on bail.
He was not charged in the UK, where the investigation into him was dropped.
Mr Love's defence team argues his depression and Asperger's syndrome mean he should not be sent abroad, but US prosecutors say he is using his mental health issues as an excuse to escape justice.
In England and Wales, the maximum sentence for crimes such as those of which Mr Love is accused is two years and eight months.
An autistic man suspected of hacking into US government computer systems is to be extradited from Britain to face trial, a court has ruled.