Lauri Love, 33, faces charges in the United States for allegedly hacking into the networks of the US Federal Reserve, US Army and NASA, among others, in 2012 and 2013.
Kaim Todner, the law firm representing Love, hailed what it called a "landmark judgement".
"The British justice system has taken the stance that we should deal with the matter ourselves, rather than accept the US government's demands," it said.
"It has also been recognised that mental health provisions in US prisons are not adequate to satisfy us that Lauri would not have come to serious harm if he were extradited," the firm said in a statement.
Judge Ian Burnett handed down the ruling, to cheers from people in the public gallery at the High Court in London.
Love, who has dual British and Finnish citizenship, was arrested at his home in Britain in October 2013.
He had appealed against a 2016 British court ruling that he could be extradited to the United States to face the charges.
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