McKinnon could be extradited to US by Christmas
Alan Johnson said he had considered demands for him to intervene in the case but had decided the extradition would not breach Mr McKinnon's human rights.
The 43-year-old, from Wood Green in north London, is accused of breaking into the Pentagon's computer system but says he was just seeking UFO evidence.
Mr McKinnon, who has Asperger's syndrome, was given hope last month when the Home Secretary agreed to study new medical evidence before deciding on his extradition to the US.
Mr Johnson's deliberations came after the High Court refused Mr McKinnon permission to appeal to the Supreme Court against his removal to America.
Mr McKinnon's family say that his health has deteriorated significantly under the pressure of the pending extradition and fears about how he will be treated by the US authorities.

Alan Johnson rejected new appeal
Now in a statement, Mr Johnson said: "I have carefully considered the representations in the case of Gary McKinnon.
"The information is not materially different from that placed before the High Court earlier this year and does not demonstrate that sending Mr McKinnon to the US would breach his human rights."
He added: "As the courts have affirmed, I have no general discretion. If Mr McKinnon's human rights would be breached, I must stop the extradition. If they would not be breached, the extradition must go ahead."
Mr McKinnon's mother, Janis Sharp, said Mr Johnson and the Government "should hang their heads in shame".
"To force a peaceful, vulnerable, misguided UFO fanatic like Gary thousands of miles away from his much-needed support network is barbaric," she said.
"This is a cruel and miserable decision. If the severity of Gary's medical condition isn't sufficient to prevent his extradition, I can't imagine what is. "God help others facing a similar fate. I'm so upset and angry."
Ms Sharp said her legal team would now apply for a judicial review, but if that was not granted then her son could be extradited before Christmas. "What a heartless and cowardly decision this is," she added. (That's a polite way of putting it!)
Every time this sneaky little shit makes a move, he proves himself to be a spineless cunt with the morals of a snake - no wonder he's been keeping such a low profile for the last few weeks! Alan "I'm just a hack politician" Johnson is even a fucking embarrassment to hack politicians everywhere - this man has no integrity whatsoever and no balls either and will do anything his master, Gordon Brown, tells him to do, and as Gordon is still busy trying to insert himself all the way into Obama's arse, this outcome was a foregone conclusion!
The sooner this pathetic, paranoid government is given the boot by the British people, the better - they have six months left, clinging onto power simply to line their pockets for as long as they possibly can and then Labour really must be consigned to the dustbin of history forever as they can never be trusted again, not least when it comes to doing the "right thing" - their favourite line of defence when they get caught out doing the wrong thing, which, as we all know, is a Labour speciality!
I honestly hope that the two-faced, lying, bad-tempered, nasty, shitty little cunt does get Brown's job as Labour leader - he's already blown his credibility with the public so he could be a huge help in the fight to keep the bastards out of power! Besides, who else have they got......David Minibrain? Ed Testicles? Batty Hattie Harpy? Ed Militwat? Bwahahahahahaha!!!
I rest my case!