Authorities in the United States have been wanting Lauri Love, who lives with his parents near Newmarket, to stand trial over charges of cyber-hacking.
The 32 year old, who has Asperger Syndrome, is the son of Alexander Love, a vicar who has worked as a prison chaplain in Suffolk.
His lawyer, Karen Todner, said: "We are delighted for this news for Lauri and will continue to do everything we can to ensure prevention of his extradition to the United States of America."
The Home Office said Home Secretary Amber Rudd authorised Love's extradition to the US last year, having ''carefully considered all relevant matters''.
The move came after a district judge at Westminster Magistrates Court ruled Love could be extradited to the United States.
The Home Office has now said Love can challenge the district judge's decision during a legal challenge at the High Court in London. The date is yet to be confirmed.
According to his lawyer, Love could face a 99 year prison sentence if he is found guilty of accusations that he targeted organisations including the Federal Reserve, the US Army, the Department of Defence, Nasa and the FBI during cyber-attacks in 2012 and 2013.
Speaking last summer, Rev Alexander Love said he feared his son would commit suicide if he was extradited to the US.