Assange has been imprisoned in Belmarsh Prison in London since 2019, when the United States tried to get him extradited.
The couple met when Assange lived in the Ecuadorian embassy in London, in an attempt to avoid extradition. They have two children together.
“I am relieved that reason has prevailed, and I hope there will be no further interference in our marriage,” Moris told the British Press Association (PA).
“Mr Assange’s request was received, assessed and processed in the usual way, as for any inmate,” said a spokesman for the prison.