The 20-bed facility is a key part of the Andrews government's pledge to shift away from dealing with public intoxication as a crime and instead treat it as a health issue.
Under the revised approach, outreach services will support people who are drunk in public and transport them to a safe place to rest and sober up if necessary, Mental Health Minister Gabrielle Williams said.
While a safe place for many would be with a family member, friend or carer, for some it would be at the centre, she said.
The policy is scheduled to take effect on Melbourne Cup Day, November 7, with work to fit out the Collingwood centre due to start soon.
Further centres and a comprehensive model focused on Aboriginal and Torres Strait Islander communities would be established across the state, Ms Williams said.
"There is a significant body of work going on at the moment to ensure we have that statewide model rolled out in time," she said.
"We need to remember that at the heart of this have been the untimely and tragic deaths of people in prison cells who arguably should never have been there in the first place."
Not-for-profit organisation Cohealth will operate the centre.
Trained staff are expected to work alongside local health and social support services to ensure those using the facility have support for other issues including drug use, family violence and homelessness.
A dedicated phone line is expected to be set up to field referrals, with people able to walk into the centre themselves or have outreach teams take them there.
Cohealth deputy chief executive Christopher Turner said the organisation was proud to be chosen to run the service, which would include the deployment of 10 mobile vans across metropolitan Melbourne.
The sobering-up service will be modelled on a successful trial in Yarra.
"From highly intoxicated young people separated from their mates after a night out to people who've had one too many after-work drinks to homeless people with addiction, this service is for everyone," Mr Turner said.
"This is not a transport service, this is a health service.
"Our first priority will be to have health workers attend and provide care and support people to get home safely."
Ambulance Victoria and Victoria Police would continue to respond to public intoxication incidents where there were emergency concerns or the community was at risk, Ms Williams said.
Opposition health spokeswoman Georgie Crozier said she didn't believe the response constituted a statewide plan and agreed with the Victorian police association's assessment of the centres as a "stuff-up".
The union has criticised the shift to a health-based approach.
Secretary Wayne Gatt said the Collingwood facility was fine for people in inner-Melbourne, but he questioned whether other Victorians would be left in the lurch.
"The question remains, what do we do with people in Footscray, Sunshine and Pakenham?" he said.
Victorian Ambulance Union secretary Danny Hill said he hoped the sobering-up centres would free up paramedics without leaving police waiting at scenes for long periods before services arrived.
"We also wait to see where the next (services) will be rolled out because the commitment is to have many more right across the state," he told AAP.
The Victorian government committed to decriminalising public drunkenness at the 2019 coronial inquest into the death of Yorta Yorta woman Tanya Day.
She was arrested for being drunk in a public place and died after hitting her head in a concrete cell at Castlemaine Police Station.
A coroner found her death was preventable.
Queensland is the only state that has not moved to decriminalise public intoxication.
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