Gary McKinnon is charged with breaking into dozens of computers belonging to NASA, the U.S. Defense Department and several branches of the U.S. military soon after the Sept. 11 attacks. U.S. prosecutors have spent seven years seeking his extradition.
The 43-year-old claims he was searching for evidence of alien life, although prosecutors say he left a message on an Army computer criticizing U.S. foreign policy.
The High Court decision denies McKinnon the possibility of taking his case to the country's new Supreme Court - the latest in a series of blows to his campaign to remain in Britain.
Lord Justice Stanley Burnton said that extradition was "a lawful and proportionate response" to McKinnon's alleged crimes and that the legal issues raised by the case were not important enough to be considered by the nation's highest court.
McKinnon's attorney, Karen Todner, said she was not giving up.
"The legal team are now considering our position and we will exhaust every avenue to prevent Gary's extradition," she said after the ruling.
She added that lawyers were considering taking the case back to the European Court of Human Rights, which has previously refused to stop his extradition.
McKinnon's supporters argue that he is autistic and should not be put through the ordeal of a custodial sentence across the Atlantic. McKinnon has offered to plead guilty to a hacking charge in Britain in order to avoid extradition, but prosecutors here turned down the legal gambit earlier this year, saying the U.S. was the proper venue for a trial.
"I've committed a crime. I've admitted to it, and I'm very sorry. I've apologized many times, but I think the American authorities' response to the crime far outweighs what would have happened to me in my own country,"earlier this year. "I'm being treated like a terrorist in America."
The case has attracted significant attention in Britain, where it has been a touchstone for debate about the country's fast-track extradition treaty with Washington - signed in the wake of Sept. 11 - and wider U.S.-British relations.
McKinnon's mother, Janis Sharp, said that her government was too willing to send its citizens to the U.S. "as sacrificial lambs" to safeguard the pair's "special political relationship."
"To use my desperately vulnerable son in this way is despicable, immoral and devoid of humanity," she said after the ruling.
Opposition lawmaker David Davis said Britain had signed up to a set of agreements which "masquerading as anti-terror laws, actually disadvantaged a whole range of British citizens."
Britain's Home Office, which would ultimately be responsible for handling McKinnon's extradition, said only that it had noted the decision. Todner said British officials had given her legal team two weeks to consider its options.