Green Party MP Jeremy Buckingham proposed the motion to the upper house of the New South Wales Parliament on Thursday.
The bill also asked the house to reflect on "the divisive, destructive impact...[of] hate speech from political candidates".
The motion passed by the court in Sydney said: “This house... agrees with those who have described Mr. Trump as a 'revolting slug' unfit for public office.”
It added the house also “condemns the misogynist, hateful comments” made by the Republican candidate about women and minorities, including remarks “that clearly describe sexual assault”.
The motion referred to a 2005 video released on Friday, in which Mr Trump talks about “grabbing women by the p***” and boasts “when you’re a star, they let you do it.”
Mr Trump apologised for his comments, but also said they were “locker room talk”.
Because nobody objected to the motion, the bill was recorded as having been unanimously agreed to by the house, Associated Press reported.
“It's great that all sides of Australian politics, from conservatives to liberals to Greens, agree that Donald Trump is a 'revolting slug' and completely unfit for public office,” Mr Buckingham said in a statement.
“It's clear that all reasonable and decent people find Donald Trump's behaviour obnoxious and that the world is hoping American voters reject his politics of hate,” he added.
On Tuesday, Australia's opposition leader Bill Shorten said the Republican candidate was not fit to be president.
“By his own words and his own actions, he has confirmed the worst fears of millions in the United States and beyond its borders - he is entirely unsuitable to be leader of the free world,” the centre-left Labor Party leader said, breaking a long-standing Australian convention of not taking sides in US political contests.
Prime minister Malcolm Turnbull, who in May criticised the Labor leader for potentially offending Americans by describing some of Mr Trump's views as "barking mad", called Mr Trump's comments about women loathsome on Monday. “They deserve the absolutely universal condemnation that they’ve received," he said.
President of the Legislative Council Don Harwin allowed the motion labelling Mr Trump a "revolting slug", deeming it not to use "unparliamentary language". Parliamentary procedure prevents MPs from using “extremely distasteful” words.
However some Australians on social media were critical of the politicians The BBC reported.
“What a spectacular waste of time. Glad to see the House discussing the real hot button issues as they relate to NSW,” said David Kelley, on Facebook.
"It amazes me how politicians are willing to tarnish relations with a future US president solely for the sake of pathetically moralising virtue-signalling," said Arden Rushwood, from Brisbane. "We didn't elect you to tell us what to think, or to insult other world leaders."
Mr Buckingham has previously courted controversy with high profile political stunts, including vaping an e-cigarette in parliament.
But on this occasion he is in good company. In the US many top Republicans, including House Speaker Paul Ryan, have distanced themselves from Mr Trump in recent days.
It is uncertain where Mr Buckingham got the term "revolting slug", but US talkshow host Rosie O'Donnell, who has a long-running public feud with Mr Trump, previously described the business man turned politician as “an orange slug”.
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