Mr Love's lawyer, Mr Edward Fitzgerald QC, told the Court of Appeal the defence was not seeking immunity from justice, but said if Mr Love was sent to the U.S. there was a significant risk he would not be fit to be tried.
Lauri Love, who has Asperger's syndrome, is accused of involvement in a series of hacks in 2012 and 2013 into computers at agencies including the Federal Bureau of Investigation, the U.S. army, the Missile Defense Agency and the Federal Reserve.
Authorities in America had been fighting for Mr Love, 33, from Stradishall, near Newmarket, to face trial on charges of cyber-hacking, which lawyers said could have meant a sentence of up to 99 years in prison if found guilty.
"It would not be oppressive to prosecute Mr Love in England for the offences alleged against him".
The Justices wrote the Crown Prosecution Service should now work with the authorities in the United States to bring a prosecution against Mr Love in the UK.
"It has also been recognised that mental health provisions in United States 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.
Love, who has joint British and Finnish nationality, has Asperger syndrome and severe depression.
"We emphasise however that it would not be oppressive to prosecute Mr Love in England for the offences alleged against him", they wrote.
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In response, Crown Prosecution Service said in a statement: "We have received the high court's judgment on Lauri Love, which we will now consider before making any further decisions".
He said outside the courthouse he hopes his case can help spur discussion about how people with mental health issues are handled by the justice system.
"This decision is important for the appropriate administration of criminal justice and also for the humanitarian accommodation of people whose brains work differently", he said. "There is an ongoing problem with people with autism in the justice system - they have actually been debating it in Westminster Hall".
British judges on Monday rejected a USA request for the extradition of a man accused of hacking into thousands of United States government computers in a ruling that could set a precedent for similar pending cases.
British charity organization Liberty, which promotes civil and human rights, assisted Love with his appeal.
"This is not just for myself", Love told press after the ruling.
"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 bad ordeal", she said.
His legal team said Love would face almost 100 years in prison if he were extradited and charged in the US.
But the extradition request was blocked on Monday. A lower court in London had approved his extradition in 2016. "However, they do not consider that making all the USA witnesses available for trial in London and transferring all of the US material to this jurisdiction would be in the interests of justice".