Stella Moris said she hoped there would be no further interference in their wedding plans after the couple previously accused the prison governor and UK Justice Secretary Dominic Raab of preventing it being held.
She visited Assange on Wednesday in Belmarsh Prison, in southeast London, where he is being held while the United States continues legal moves to extradite him.
"Today Julian and I are finally registering our intention to marry here inside Belmarsh prison. We were originally booked to do so three weeks ago," she said.
"Of course, the circumstances are not ideal but I am relieved that reason has prevailed and I hope there will be no further interference with our marriage.
"In the UK everyone who is old enough, no matter who they are or where they are from, has a basic human right to get married to whom they choose.
"This right is written into law. Julian is not charged with any crime in this country, he is not serving a sentence, his imprisonment serves no purpose at all other than to prolong and make his suffering worse."
The couple have been engaged for a number of years and have been trying to get married despite the legal action.
They have two children: sons Gabriel, four, and Max, two.
"I hope the injustice of this situation is swiftly brought to an end so that we can enjoy marriage outside of the walls of Belmarsh when he is freed," Moris said.
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