Richard O'Dwyer is wanted by U.S. authorities for copyright infringement offences in connection with his TVShack website, which did not host any illegal content but provided links to other online sites where it could be accessed.
In a London court hearing in January, his lawyers argued that by linking to other websites, he had done nothing more than the likes of Google or Yahoo.
However, a judge rejected his argument and Home Secretary Theresa May has upheld the decision to extradite the 23-year-old.
He can still appeal to London's High Court against the ruling.
Campaigners argue O'Dwyer's is the latest in a series of cases that demonstrate Britain's extradition rules with the United States are lopsided, allowing suspects to be extradited without criminal charges from British authorities.
The most high-profile is that of British computer hacker Gary McKinnon, who was arrested in 2002 after allegedly hacking into U.S. security systems including the Pentagon and NASA and who is still fighting to avoid extradition.
"Today, yet another British citizen is being sold down the river by the British Government," O'Dwyer's mother Julia was quoted by media as saying.
Before his court hearing in January, O'Dwyer told media that he started the project to improve his computer programming skills and help him get a work placement. The student said he sold advertising space to pay for the server fees.
U.S. authorities, who have cracked down far harder on illegal file-sharing to protect its film, television and music industries, said he had earned $230,000 from the venture.
"The district judge found the allegations were comparable to an offence under UK law and it was appropriate for any trial to be held in the U.S.," a Home Office spokesman said.
(Reporting by Michael Holden; Editing by Ben Harding)
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