"We are hopeful that other people will be able to rely on this". Outside, supporters gathered with signs reading "Free Love" and "Trial at home".
Liberty, which was among the groups making representations in the case, said it was "delighted" with the result.
A spokesman for Mr Love's solicitors, Kaim Todner, said it was "important" the British justice system "has taken the stance that we should deal with the matter ourselves, rather than accept the USA government's demands".
"Mr Fitzgerald QC for Mr Love was at pains to emphasise that Mr Love did not seek impunity for the acts alleged against him, but contended that he should be tried and, if convicted, sentenced in the United Kingdom", said the judges today in their written ruling. Psychologist Simon Baron-Cohen described him as "a man with several severe disabilities" during his initial extradition hearing in 2016.
Love's legal team had argued he should face charges in Britain, pointing to new rules that make it easier for British courts to try people for crimes committed there but involving other countries.
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. In fact, the UK High Court has heard that there was a severe risk Lauri Love would attempt suicide before he was extradited.
Swartz, a USA computer programmer and freedom of information activist, committed suicide in 2013 after the United States charged him with wire fraud after a large trove of academic journal articles were illegally downloaded and shared online. His lawyers said it would be "unjust and oppressive" to send him to the U.S.to face trial.
A psychiatrist, Professor Baron-Cohen of Cambridge University, prepared a report on Love that was read by the judges.More news: South Korea Deploys 50000 Soldiers to Protect Against Terror Attacks
That issue, of course, is whether the extradition and United States court process would have a serious impact on his physical and mental health.
"If he is taken to America he is going to be incarcerated in an American system which is not geared up for that kind of support".
The 32-year-old British-Finlander, who lives with his parents near Newmarket in Suffolk, was accused of carrying out a "series of cyber attacks against the websites and computer systems" of a raft of USA government agencies and private firms.
Instead Lord Chief Justice Lord Burnett and Justice Ouseley permitted his appeal against his extradition, stating it would "not be oppressive" to "prosecute Love in England for the offences".
She identified a high risk of suicide but did not bar the move, on the condition that it could be managed in American facilities.
"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.
"We believe that if he is extradited, there is a great probability that he will end his own life".