Assange, 50, is fighting attempts to remove him from the UK to face trial in the United States over the publication of secret files relating to the wars in Iraq and Afghanistan.
Last week, the UK Supreme Court turned down a request to hear his appeal against the move, bringing the long-running legal saga nearer to a conclusion.
Assange and Moris announced their engagement in November and were given permission to marry at Belmarsh prison in southeast London where he is on remand.
The Don't Extradite Assange (DEA) group said the wedding would be conducted by a registrar, with just four guests, two witnesses -- and two security guards -- in attendance. The guests will have to leave immediately after the ceremony.
Vivienne Westwood, the British fashion designer who has been a long-standing supporter of the Australian publisher, has designed Moris' wedding dress, the DEA group said.
She has also provided a kilt for Assange in a nod to his Scottish heritage, it added.
British fashion designer Vivienne Westwood is a long-time supporter and has provided the couple's wedding attire.
Moris, who is in her late 30s and has two young sons with Assange, will cut a wedding cake and make a speech outside the prison in front of their supporters.
Assange has become a figurehead for media freedom campaigners, who accused Washington of trying to muzzle reporting of legitimate security concerns.
If found guilty of violating the US Espionage Act by publishing military and diplomatic files, he could face the rest of his life in prison. For critics, however, he is seen as having been reckless with classified information that may have endangered the lives of sources.
Assange initially won a ruling against his extradition, after his lawyers successfully argued he would be a suicide risk if he were transferred to the United States.
Moris, who has two young boys with Assange, has been leading the campaign for his release
But the US government appealed, and persuaded judges that he would not be held in solitary confinement at a high-security federal detention facility.
He has spent most of the past decade in custody or holed up in Ecuador's London embassy, trying to avoid another extradition after Sweden sought his transfer to answer claims of sexual assault. That case was later dropped.
After the Supreme Court blocked his application, UK Home Secretary Priti Patel will make a final decision on the case, unless Assange's lawyers launch another challenge on a separate point in the case.