Director of Public Prosecutions Keir Starmer QC said the chances of a successful conviction were "not high".
He announced the decision some three months after Home Secretary Theresa May stopped the extradition.
Mr McKinnon, 46, admits accessing US government computers but says he was looking for evidence of UFOs.
The US authorities tried to extradite him to face charges of causing $800,000 (£487,000) to military computer systems and he would have faced up to 60 years in prison if convicted."
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