Lauri Love, 33, has for several years been battling extradition to face multiple charges for allegedly hacking into the networks of the US Federal Reserve, US Army and NASA, among others, in 2012 and 2013.
Love, who has dual British and Finnish citizenship, suffers from Asperger's syndrome and has also been diagnosed with depression.
Speaking afterwards, Mr Love's father, Rev Alexander Love, who sat next to him in court, said: "We are just glad that it's happened".
The lord chief justice, Lord Burnett of Maldon, and Mr. Justice Ouseley handed down their judgment at the Royal Courts of Justice on 5 February.
Supporters cheered and clapped as the decision was announced, while Mr Love hugged his mother, Sirkka-Liisa Love, and his father wept.
"I'm not saying that I'm looking forward to being prosecuted but I think that there is a better chance that it will be done justly and fairly here in the UK", Love said.
Mr Love was allegedly involved with #OpLastResort, which saw global hackers target the U.S. government following the suicide of American computer scientist Aaron Swartz.
The Rev Love said he was concerned his son would not get the support he needed if he was jailed in the United States, adding "the metal health provision in American prisons, from what I have read, is woefully inadequate compared to ours".
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His lawyers argued that extraditing him to the United States, where he could eventually face up to 99 years in prison on hacking charges, would create a high risk of his committing suicide. "Much of Mr Love's argument was based on the contention that this is indeed where he should be prosecuted".
A Westminster magistrate approved his extradition in September 2016, but Love appealed against it after home secretary Amber Rudd subsequently ordered his extradition last November.
Emma Norton, head of legal casework for British human rights group Liberty, who intervened in the case, said: "Where unlawful activity is alleged to have taken place in the United Kingdom, those suspected should be tried in the United Kingdom - not packed off to foreign courts and unfamiliar legal systems".
The High Court appeal centred on that ruling made by District Judge Nina Tempia.
"The CPS (Crown Prosecution Service) must now bend its endeavours to his prosecution, with the assistance to be expected from the authorities in the United States, recognising the gravity of the allegations in this case", they wrote.
The case was seen as important for the "forum bar", a defence against extradition introduced after Aspergers sufferer Gary McKinnon.
He was facing decades in U.S. prison at the time of his death.
"This ruling is a massive victory for free expression online", said Naomi Colvin, director of The Courage Foundation, an organisation that supports people persecuted in cases that involve issues of freedom of information.