Officers from the NSW Police Force Terrorism Investigation Squad arrested the man at Sydney's international airport on Thursday after receiving a tip-off from the public.
Damien James O'Neil arrived in the country on a plane from London and was taken to Mascot Police Station following his arrest.
Acting Deputy Commissioner Frank Mennilli said he could not go into detail while the matter was before the courts, but that the man "did post on social media a number of threats of some possible activity that he could be undertaking".
A home at Chippendale and a storage facility in Sydney's inner-west were searched, and items including documents and hard drives were seized, police said.
O'Neil's case has been mentioned in the Parramatta Local Court but he did not apply for bail.
He is due to reappear on January 10.
Acting Deputy Commissioner Mennilli said the man did not have links to any cultural groups.
"He has been charged with a Crimes Act offence, not a terrorist offence," he said.
"The matter is still under investigation and there may be some further charges, but I can certainly assure everyone there is no current threat from that individual or any other person."
Public should be vigilant while still enjoying festivities, police say
In a statement, Deputy Police Commissioner Catherine Burn said initial investigations suggested it was an isolated incident.
"We are confident that there are no current or specific threats to New Year's Eve, and while we ask people to remain vigilant, people should enjoy the celebrations," she said.
"The community should be also reassured that we will take swift action to ensure the ongoing safety of the public."
City of Sydney councillor Jess Scully said there will be a strong police presence during the evening.
"I think it's always really difficult these days when you have large public gatherings and security is something that is top of mind," she said.
"I know it's something that we're working really closely with the New South Wales Police."
Last week, Victorian police foiled an alleged terrorist plot to detonate explosive devices around Melbourne, possibly on Christmas Day.
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