Alex Kobi James-Devine was leaving the area outside the Observatory Bar on Hobart's waterfront on February 8 when he made the gesture towards officers.
He pleaded guilty to performing a Nazi gesture as well as charges of behaving in a violent manner, failing to comply with police officer directions and disorderly conduct.
During sentencing in Hobart Magistrates Court on Friday, magistrate Andrew McKee said James-Devine had for a period of his life fallen into "Nazi ideology" online.
He had since "removed himself" and now attends church where he enjoys a sense of community, Mr McKee said.
James-Devine was heavily intoxicated on the night in question, and had earlier been punched in the face and lost a tooth during an altercation.
He "fell back into old habits" when performing the gesture, Mr McKee said.
James-Devine told the court it was "just like an F U type of thing".
The offence carries a maximum penalty of three months' jail and a $4000 fine.
James-Devine was fined $1400 and a conviction was recorded, with Mr McKee noting it was clearly an offensive gesture and there was no justification for it ever being made.
"Other members of the public would have seen the gesture ... others might find it extremely offensive," he said.
A conviction was recorded on all four charges, with the magistrate noting the maximum penalty doubles if someone is convicted of making a Nazi gesture a second time.
General deterrence was an important factor in sentencing, he said.
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