The 20-year-old, born in Australia to Somali parents, was detained in a raid on a house in the Melbourne suburb of Werribee on Monday. He is expected to be charged later Tuesday.
Police claim he accessed a guide book online produced by Al-Qaeda on how to commit terror acts and use firearms, but was arrested before he could purchase an automatic rifle.
"What we will be alleging is that he was intending to use a firearm to shoot and kill as many people as he could in the Federation Square area on New Year's Eve," said Victoria Police Deputy Commissioner Shane Patton.
"It is a tremendous concern to us that (during) the festive season, when people are out enjoying themselves, that there is a potential plot to commit a terrorist act. That is a huge issue for us but that is why we put the resources in."
He said the arrest meant the threat "has been removed".
Federation Square is in the heart of the city, opposite busy Flinders Street train station and St Paul's Cathedral. It is one of the most popular places to see in the new year and would be packed on December 31.
The foiled plot comes a year after police prevented another attack in the same area on Christmas Day, arresting several men who planned to use explosives, knives and guns to target the location.
Patton said the man, who lived with his parents, had been on their radar since the beginning of the year, part of a small community of extremists that police have been monitoring.
His behaviour had gradually escalated over time, but police believe he was acting alone.
"The potential of the attack was catastrophic," said Patton, adding that the man was an "ISIS sympathiser".
Asked if he had been inspired by last year's Christmas Day plot, Patton said how he became radicalised was still being investigated.
"We will be exploring where this person of interest got the idea from," he said.
"Certainly, he becomes particularly energised when he sees other activities in the terrorist arena occurring."
Australian officials have grown increasingly concerned over the threat of extremist attacks, raising the national terror alert level to "probable" in September 2014.
Since then, 74 people have been arrested in 347 counter-terror investigations.
Authorities say 13 attacks have been prevented in the past few years, including an IS-directed attempt to bring down a plane using poisonous gas or a crude bomb disguised as a meat mincer.
Despite this, several attacks have taken place, including a cafe siege in Sydney in 2014 where two hostages were killed.