Mr McKinnon, 46, who admits accessing US government computers but claims he was looking for evidence of UFOs, has been fighting extradition since 2002.
The home secretary told MPs there was no doubt Mr McKinnon was “seriously ill” and the extradition warrant against him should be withdrawn.
Mrs May said the sole issue she had to consider was his human rights.
She said it was now for the Director of Public Prosecutions, Keir Starmer QC, to decide whether he should face trial in the UK.
Mrs May said: “Since I came into office, the sole issue on which I have been required to make a decision is whether Mr McKinnon’s extradition to the United States would breach his human rights.
“Mr McKinnon is accused of serious crimes. But there is also no doubt that he is seriously ill.
“He has Asperger’s syndrome, and suffers from depressive illness. The legal question before me is now whether the extent of that illness is sufficient to preclude extradition.
“After careful consideration of all of the relevant material, I have concluded that Mr McKinnon’s extradition would give rise to such a high risk of him ending his life that a decision to extradite would be incompatible with Mr McKinnon’s human rights.”