Karen Todner, McKinnon's lawyer, said, "I hope this may be a signal of a more compassionate and caring home secretary and one who is willing to defend the rights of our citizens."
Todner said she would be lodging further representation shortly. "In the meantime, Gary will remain in the UK," she said.
May's decision follows earlier representations on McKinnon's behalf, and widespread press coverage over the weekend. According to Todner, May wanted more time to consider the issues in the case.
In the run up to the election, both Conservatives and Liberal Democrats expressed their antipathy for the way McKinnon's case had been handled.
The US has accused McKinnon of the "greatest hack of all time", after he broke into Pentagon and other federal computer systems around the time of the 9/11 atrocity. However, the US delayed a request for his extradition until 2005, when a new extradition treaty, widely regarded as one-sided, came into effect.
McKinnon, an Asperger's sufferer, has admitted hacking the US computers. He has always asked to be tried in the UK and said he was prepared to serve a sentence in a UK jail.
In the US he faces up to 60 years in jail, while in the UK any sentence under the Computer Misuse Act is likely to be much shorter.
This article was originally published by Computer Weekly