McKinnon was first indicted by an American grand jury in November 2002 for hacking into US military computers, including the Pentagon and NASA, from his north London bedroom while he was looking for UFOs. He could have faced a prison sentence of up 70 years under US law.
The extradition order against McKinnon has been withdrawn and it will now be for the Director of Public Prosecutions to decide whether he should be prosecuted in Britain.
A spokeswoman for the State Department, Victoria Nuland, said: "The United States is disappointed by the decision to deny Gary McKinnon's extradition to face long overdue justice in the United States. We are examining the details of the decision."
The US authorities have described McKinnon's actions as the "biggest military computer hack of all time". The Washington Post observed that the decision "could ignite tensions in an otherwise close transatlantic relationship", while the former White House counsel Douglas McNabb said the United States Attorney would be furious.
The decision, which is the first time an extradition has been halted under the 2003 US-UK treaty, prompted immediate delight from those who campaigned to prevent McKinnon's removal, and politicians from all parties.
Britain's Deputy Prime Minister Nick Clegg said he wanted to pay tribute to Sharp's determination to speak up for her son over 10 years. "I've long argued that I think it would have been wrong to send someone as vulnerable as Gary McKinnon to the United States and also I'm delighted that the Home Secretary has set out some plans about how we rebalance the extradition arrangements between the UK and the USA," he said.
The only discordant note came from the former Labour home secretary Alan Johnson, who said the hacker's human rights case had been rejected by judges in 2009 and claimed May had made the decision "in her party's best interest; it is not in the best interests of the country". He disclosed that the US authorities had been prepared to allow McKinnon to serve his sentence in a British prison when Johnson rejected McKinnon's earlier appeals.
May confirmed to MPs her intention to scrap the home secretary's discretion under the Human Rights Act that enabled her to prevent McKinnon's extradition. "Matters such as representations on human rights grounds should, in future, be considered by the High Court rather than the home secretary.
"This change, which will significantly reduce delays in certain cases, will require primary legislation."
She opened the door for more wide-ranging reform of the extradition process to reduce delays of up to 14 years by looking again at the provision of legal aid for terror suspects in national security cases and introducing a permission stage for appeals to UK courts.
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