Gary McKinnon's MP said the Home Secretary had "saved his life" in withdrawing his extradition order.
Conservative MP David Burrowes said he was "delighted" at the decision to spare the computer hacker from being taken to the US to face trial, minutes after Theresa May made a statement to the House of Commons.
Burrowes, who had threatened to resign if McKinnon would be extradited, said: "After 10 long years Gary can at last get his life back."
McKinnon, who has Asperger's syndrome, has been accused by US prosecutors of "the biggest military computer hack of all time", but he claims he was simply looking for evidence of UFOs.
McKinnon was labelled as 'the biggest military computer hack of all time' by US prosecutors
Speaking to The Huffington Post UK on Tuesday, the mother of Richard O'Dwyer, the 24-year-old who faces extradition over piracy, said May's decision was "fantastic, excellent news."
But Julia O'Dwyer questioned why the home secretary introduced a forum bar which would not apply to her son's pending case.
"They have it within their power to do so [to apply legislation retrospectively]. Scott Baker [the judge who reviewed extradition laws in 2011] stated that.
"We're not asking for Richard to be not prosecuted, we're just asking for him to be dealt with in this country," she told The Huffington Post UK.
Karl Watkin MBE, an international businessman who has spent the last 12 years campaigning against the UK's extradition treaty with the States, said that Theresa May had made "a cynical political decision" despite the "great result."
"The Home Secretary was desperate for a hook to hang her u-turn on and thankfully found one.
"Sadly this will not benefit others including Richard O'Dwyer. The UK needs to stand up to the extraterritorial reach of the US in particular on cyber crime which should be prosecuted where it physically took place not on the tenuous location of servers," he told The Huffington Post UK by email.
"The extradition treaty remains fundamentally flawed. UK citizens alleged to have committed crimes in the UK should be tried here, Richard O'Dwyer is the next case in point and should be tried in the UK for his alleged crime"
Melanie Riley, of the campaign group Friends Extradited, said she was "relieved and delighted for Gary and his family and his lawyers. A brave and correct decision has finally been made by the Home Secretary."
Jeremy Croft, Head of Policy and Government Affairs, said: “It is welcome news that the Human Rights Act is being used exactly as it is intended to be used - to protect vulnerable people when their human rights are at risk.
“It makes a refreshing change to hear Theresa May invoking the human rights protections afforded by the Human Rights Act. It can only be hoped that her decision today marks a change in direction wherein the Home Secretary ceases to call for those very protections to be dismantled, and indeed champions the Act for the safeguards it provides.”
“Our thoughts today are with all those friends unnecessarily extradited before the wrongs of the Extradition Act 2003 are put right," she said.
Shami Chakrabarti, Director of human rights group Liberty, said in a statement it was a "great day for rights, freedoms and justice in the United Kingdom. The Home Secretary has spared this vulnerable man the cruelty of being sent to the US and accepted Liberty’s long-standing argument for change to our rotten Extradition laws.
“Extradition should prevent fugitives escaping – not allow for Britons like Gary to be parcelled off around the world based on allegations of offences committed here at home.
“This campaign, led by Gary’s fearless mother, united lawyers, politicians, press and public from across the spectrum in the cause of compassion and common sense."