However, the timing of the move has raised concerns from the state’s police force.
The changes will come into effect from November 7, which coincides with the annual Melbourne Cup public holiday.
She had been arrested for public drunkenness when she was found asleep on a train travelling from Bendigo to Melbourne.
Premier Daniel Andrews said the laws were designed to stop people being sent to jail cells to sober up.
“Locking people up because they are drunk is not a sign of success, that is a sign of failure and not a health led response,” he said.
“We got it wrong and we need to do better on issues like (Tanya Day)”.
Police Association secretary Wayne Gatt told 3AW that although he supports the decriminalisation of public drunkenness, the timing wasn’t ideal.
“We understand why the government wants to decriminlise public drunkenness. We support that and it makes sense,” he said.
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“The timing and way it is done, is what concerns us.”
Gatt said to lift the public drunkenness laws on Melbourne Cup Day would however be “a baptism of fire”.
“What are we going to do, what are our powers we are going to use once it’s no longer an offence?”
“We agree it shouldn’t be an offence.
“But you should have residual powers for police so they can actually do something, because those sorts of people are very unlikely to just go home willingly when a person from an outreach team turns up.
“They’re going to be met with the very same response police have been met with for decades.”
The move brings Victoria into line with other Australian states, except for Queensland.