He had also asked the court to rule on whether his Asperger's Syndrome meant he could not be extradited to the US.
His lawyers argued extradition was "unnecessary, avoidable and disproportionate" and had not taken place in other cases.
But, in a 41-page ruling, the judges said extradition was "a lawful and proportionate response to his offending".
Home Secretary Alan Johnson said: "Mr McKinnon is accused of serious crimes and the US has a lawful right to seek his extradition, as we do when we wish to prosecute people who break our laws.
"The court judgement has also made absolutely clear that the DPP's decision not to prosecute in the UK was the right one.
"My predecessor has already sought and received clear assurances from the US that Mr McKinnon's health and welfare needs would be met, should he be extradited.
"It is open to Mr McKinnon to seek to appeal to the House of Lords."
Mr McKinnon faces up to 70 years in prison if convicted in the US of what prosecutors have called "the biggest military computer hack of all time".
He has always insisted he was looking for classified documents on UFOs which he believed the US authorities had suppressed.
Speaking outside the High Court, his mother, Janis Sharp, said her son - who did not attend court - had been "naive enough to admit to computer misuse without having a lawyer and without one being present".
US-UK EXTRADITION TREATY
2003 treaty, agreed in aftermath of 9/11 attacks
Offence must be punishable by one year or more in jail in both countries
US has to prove "reasonable suspicion" for extradition of a British citizen
To extradite an American from the US, British must prove "probable cause"
Since 2004, 46 people have been sent from the UK to the US for trial, and 27 from US to UK
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