Mr McKinnon faces 60 years in jail if convicted in the US
A High Court judge is to rule on whether Home Secretary Alan Johnson was wrong to allow the extradition of computer hacker Gary McKinnon.
The judicial review will examine Mr Johnson's decision that a US trial would not breach his human rights.
Mr McKinnon, 43, who has Asperger's syndrome, is accused of breaking into the US military computer system. He says he was seeking evidence of UFOs.
The Home Office said it had "noted" the court's decision.
A hearing is likely to take place in April or May.
Mr McKinnon's lawyer said she was "delighted" that they had been granted permission for judicial review, but warned that her client was in a "very poor mental state" due to stress.
Solicitor Karen Todner also appealed to Mr Johnson to reverse his decision and asked US President Barack Obama to withdraw the request for extradition.
"Mr McKinnon's suffering has gone on long enough," she said.
The Glasgow-born man's mother, Janis Sharp, said she felt "incredible, indescribable" relief.
"I can't believe it - some common sense at last. This judge has made such an honourable and decent decision.
"We've fought for so long for compassion and understanding. Gary's health has badly declined, it's been traumatic to see," she said.
In November, Mr Johnson said he could not block the move to a trial in the US on medical grounds, saying he had "no general discretion" to refuse the request from the US government.
The computer systems Mr McKinnon, now of Wood Green, north London, is accused of breaking into include the Pentagon. If convicted, he faces 60 years in prison.
A Home Office spokesman said: "As the case is before the courts, we do not propose, pending the outcome, to comment further."
Liberal Democrat Leader Nick Clegg said the judicial review was "heartening news".
"Even now the Prime Minister and Home Secretary could step in to spare Gary McKinnon from this ordeal by ensuring that he is instead tried in a British court.
"It must be hoped that the courts prevent this unfair extradition and in doing so display more courage than our ministers," he said.
Isabella Sankey, director of policy for human rights group Liberty, said the charity welcomed the decision.
"We should not be sending people to be tried in foreign courts and then, if convicted, imprisoned away from family and friends when it is perfectly feasible to try them in the courts in this country," she said.
Mr McKinnon's lawyers and family have fought a series of long-running court battles in an attempt to avoid extradition.