The law makes it an offence punishable by up to 12 months in prison to publicly perform the Nazi salute or display the Nazi swastika or the double-sig rune associated with the Schutzstaffel (SS) paramilitary group.
The sale and trade of these symbols is similarly prohibited.
Attorney General Mark Dreyfus said in a statement the legislation sent a clear message there was no place in Australia for those who glorify the Holocaust or terrorist acts.
"This is the first legislation of its kind and will ensure no one in Australia will be allowed to glorify or profit from acts and symbols that celebrate the Nazis and their evil ideology."
Introduced in June and passed in December, the law has taken on new significance amid a surge in antisemitism and Islamophobia following the October 7 attack by Hamas, in which some 1200 were killed and 240 taken hostage, according to Israeli officials.
Unverified footage showing a small group of men outside the iconic Opera house shouting "gas the jews" during a pro-Palestinian protest in October triggered outrage around the world and a police investigation.
Separately, police arrested three men in October for performing the Nazi salute outside the Jewish Museum of Australia. There were more anti-Jewish incidents in October and November last year than the twelve months prior, according to the Executive Council of Australian Jewry.
The new law also bans the public display or trade in symbols associated with prohibited terror organisations, such as Islamic state, Hamas or the Kurdistan Workers' Party (PKK).
Exemptions exist for academic, educational or artistic use.
