McKinnon lost his case in the Court of Appeal in April, while trying to overturn the House of Lords to extradite him.
Barrister Ben Cooper of Charter, who heads up McKinnon's legal team, said his client was "delighted to learn of this important development."
The US government claims his actions in 2001 and 2002 damaged 97 computers and caused US$700,000 worth of damage.
McKinnon doesn't deny hacking into Nasa and US military networks, but claims he only broke in to uncover information about extraterrestrial technology he believed the authorities were hiding from the public.
He has asked to be tried in the UK as his crimes were committed in this country.
During the legal process, McKinnon has accused the US of trying to blackmail him into accepting voluntary extradition and acting in an "oppressive" and " arbitrary" way.
McKinnon's extradition was originally signed off in July 2006 by home secretary John Reid.
At that time originally he was surprised at the speed of the decision.
"I was under the impression that the home secretary would have taken longer to make a decision," McKinnon said.
"It's annoying, because that would have given us more time to sort out a judicial review."
No date has been set for the hearing in the House of Lords.
Nasa hacker McKinnon appeals to the House of Lords
By Matt Chapman on Aug 3, 2007 1:10PM