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Molloy had previously pleaded not guilty, but today entered a guilty plea through his counsel, David Jones QC.
He will appear in court for sentencing on August 27, where Jones indicated Molloy would apply for a discharge without conviction.
Molloy also faced a second related charge, but this was withdrawn by police.
Millane, who had been travelling the world, met her killer in Auckland on dating app Tinder before they shared drinks at a few bars on the eve of her 22nd birthday in December 2018.
CCTV showed the pair appeared to be enjoying each others' company as they returned to his small downtown Auckland apartment.
But the university graduate would never leave the room alive - her body later found dumped in a shallow grave in the Waitākere Ranges.
Her killer, who still cannot be named for legal reasons, was convicted of murder last November for strangling Millane to death in an Auckland hotel room.
In February he was sentenced to life in prison with a minimum period of 17 years for murdering the British backpacker.
In March he announced he was appealing the conviction and sentence.
Molloy, the well-known restaurateur who owns HeadQuarters in the Viaduct, is the first person to be charged by New Zealand police after numerous suppression breaches before and after last November's high-profile trial.
Others have been given warnings by police for allegedly naming the killer.
Despite the suppression order, in the hours and days after the verdict overseas media and social media users - including in New Zealand - published the killer's name.
While breaking a suppression order is not an extraditable offence for those who do so overseas, people in New Zealand who are guilty face up to six months' imprisonment or a $25,000 fine.
In the case of a company breaching, a fine of up to $100,000 can be imposed.
The recent breaches, largely by those here and the United Kingdom, come after a year of debate about the effectiveness of New Zealand's suppression orders in the internet age.
After Millane's killer first appeared in court in December 2018, British media named him in its papers, online and on-air.
Internet behemoth Google breached a suppression order when it named Millane's then accused murderer in its "what's trending in New Zealand" mass email to New Zealand subscribers.
The email said there had been more than 100,000 searches on its search engine of the man's name.
The Google breach was met with condemnation by Justice Minister Andrew Little, who held a meeting with Attorney-General David Parker and executives from the Silicon Valley-based company.
In July last year, Google suspended its trending emails in New Zealand and apologised to Little.
After the murder trial, Little said the breaches were "really disappointing" but was optimistic changes to the way court suppression orders were enforced were on the way.