The 40-year-old allegedly made the threats on social media.
Police have also raided a house and storage facility in Sydney, where they seized documents and computer hard drives, the BBC said.
The arrest comes just a week after police said they had foiled a major terror plot which was understood to have targeted central Melbourne.
Seven people were arrested in relation to the planned attack, which had been allegedly due to take place on Christmas Day.
'Threats' made to Sydney's New Year's Eve celebrations
Destinations
Sophie Griffiths
30 December 2016
A man has been arrested at Sydney airport as he arrived on a plane from London, after Australia anti-terror police accused him of making threats against Sydney’s New Year’s Eve celebrations.
Australia has been one of the top-selling destinations for Audley
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