The appeal judges opposed his extradition on the grounds that it would be "oppressive by reason of his physical and mental condition", the BBC reported.
American officials have a fortnight to ask for an appeal in the UK Supreme Court.
But on Monday, the appeal judges told the Crown Prosecution Service to try Love in England.
Love said: "I'm hoping that this outcome can contribute to the discussion we are having as a society about how to accommodate people that have neuro-diversity, whose brains are made up in a slightly different way.
"There is an ongoing problem with people with autism in the justice system – they have actually been debating it in Westminster Hall.
"I hope in the future to be able to contribute to a slightly better understanding of the stigma associated with depression."
Love was first taken into custody in 2013 on suspicion that he had breached the networks of the FBI, the Federal Reserve and NASA.
Lord Chief Justice Lord Burnett and Mr Justice Ouseley said Love, who also suffers from depression, "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".
"We accept that the evidence shows that the fact of extradition would bring on severe depression, and that Mr Love would probably be determined to commit suicide, here or in America."
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 UK, those suspected should be tried in the UK – not packed off to foreign courts and unfamiliar legal systems. This is especially important in cases of vulnerable people like Lauri Love.
"We are delighted that the court has recognised Lauri's vulnerability, close family connections to the UK and the potentially catastrophic consequences of extraditing him. This was always a case that could have been prosecuted here and it's shameful that Lauri and his family have been put through this terrible ordeal."
Another British infosec expert, Gary McKinnon, was not extradited for accessing US Government computers in 2012, after a 10-year legal battle, because he was considered to be “seriously ill”.
The decision against his extradition was made by the current British Prime Minister Theresa May who was home secretary at the time.
A third British security researcher, Marcus Hutchins, is awaiting trial in the US, after being arrested in Las Vegas in August last year after he had boarded a plane to leave the US after attending the annual DEFCON security conference.
The chargesheet against him says he wrote and helped distribute a banking trojan named Kronos along with an unnamed co-conspirator.
The US is mad because they can’t Team America World Police the Internet. If your defence against people remote desktoping to your military systems with password ‘password’ is attempting to lock up kids.. get some actual technical defence.— Kevin Beaumont (@GossiTheDog) 5 February 2018