Love has been facing computer hacking charges filed in the US since 2013, when US authorities accused him of hacking and stealing data from the networks of the FBI, the US Army, NASA, the US Federal Reserve, the Environmental Protection Agency, and other government agencies.
Love, who denies any wrongdoing, risks a 99-year jail sentence if he faces trial in the US.
It is also still possible for the CPS - which would act on behalf of United States authorities - to take the case to the Supreme Court in a continued fight for extradition from the UK.
Love's two main grounds of appeal were that a United Kingdom law known as the "forum bar" legally prevented his extradition, on the basis that his alleged crimes were committed while he was in the United Kingdom, and that sending him into the American justice system would put him at an elevated risk of suicide because of his diagnosed Asperger's syndrome.
Speaking outside of court after the verdict, Love said he hopes the ruling would set a precedent.
Love, who has Asperger Syndrome, also suffers from severe eczema that is resistant to antibiotics, and has major depression.
His father Alexander Love said: "This is a victory for justice".
However, the decision lays the groundwork for British prosectors to take on the case, with the judges noting "it would not be oppressive to prosecute Love in England for the offences alleged against him".
Love, who has Asperger syndrome, won the right to appeal in April 2017.
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There has been a major development in the long-running fight by British student Lauri Love to avoid extradition to the United States, where he has been accused of hacking into various government websites.
Lord Burnett of Maldon wrote in his decision that prosecution of Love in England was not "oppressive" given his mental condition.
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 U.S. government's demands". The High Court appeal centred on that ruling made by District Judge Nina Tempia.
"We are hopeful that other people will be able to rely on this".
Its statement said: "This has been a landmark judgment, not just because it is the first time that the Forum Bar has successfully been argued, but also because it is a very rare occasion on which the English courts have discharged a requested person on a United States extradition request".
Having identified a high risk of suicide, she [the district judge] "properly assessed whether and how that risk could be managed were the appellant to be extradited".
His extradition was ordered by British Home Secretary Amber Rudd in November previous year after he was unable to persuade a judge that he should be tried in the UK.
Naomi Colvin, of the Courage legal support group, added: "the campaign's slogan has been "a trial at home" - that's what we've been asking for".