The website did not itself host unlawful downloads or video streams, but acted as a directory of links to others that did, Westminster Magistrates' Court heard.
American authorities allege that Mr O’Dwyer made more than $230,000 by selling advertising on TVShack in three years until December 2010.
District Judge Quentin Purdy rejected all three of the defence’s arguments against extradition, including claims Mr O’Dwyer would not get a fair trial in the United States and that if a crime was committed he should be prosecuted in Britain.
O'Dwyer's mother Julia said she was: "Very disappointed, in fact disgusted," with the verdict.
She also expressed disappointment towards the government: "for signing us up to this treaty which has opened the flood gates to America to come and seize British citizens without even having set foot outside of this country."
"That extradition law needs fixing fast," she added.
Mrs O’Dwyer added that her son intends to immediately lodge an appeal at the High Court. The extradition must first be approved by the Home Secretary, however.
Speaking outside court, Richard O'Dwyer said he had: "faith in the High Court in making the right decision," and didn't regret starting the website because it had "helped him no end" with his studies.
Richard O'Dwyer's case will pile more pressure on the government to change the rules to make it more difficult to extradite Britons to America. Last month MPs voted for “urgent reform”.
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