The 20-bed facility is a key part of the Andrews government's commitment to shift away from dealing with public intoxication as a crime and treating it as a health issue.
Under the revised approach, outreach services will support people found to be under the weather 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 new policy is scheduled to take effect on Melbourne Cup day, November 7, with work to fit out the Collingwood centre slated 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," Ms Williams told reporters.
"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 general services stream of Victoria's health-based approach to public drunkenness, including the centre.
Specially 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 drugs, family violence and homelessness.
A dedicated phone line is expected to be set up to field referrals, with people slated to be able to walk into the centre themselves or have outreach teams take them there.
Co-health was proud to be selected to run the health-based response which would include deploying mobile vans across metropolitan Melbourne, deputy chief executive Christopher Turner said.
The sobering up service would be modelled off its successful trial in the City of Yarra.
"From disorientated young people who've lost their mates late at night to people who've had one too many after-work drinks and people who are homeless and alcohol-affected, our service will be for everyone," Mr Turner said.
Ambulance Victoria and Victoria Police would continue to respond to public intoxication where there were emergency concerns or community safety 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 Police Association of Victoria's assessment of the centres as a "stuff-up".
The union has previously criticised the shift to a health-based approach.
Secretary Wayne Gatt on Friday said the Collingwood facility was fine for people in inner-Melbourne but he questioned whether those in regional Victoria would be left in the lurch.
Victorian Ambulance Union secretary Danny Hill hoped the sobering up centres would free up paramedics and wouldn't lead to police having to remain at a scene for long periods while waiting for transport services to arrive.
"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," Mr Hill told AAP.
The Victorian government committed to decriminalising public drunkenness at the 2019 coronial inquest into the death of Yorta Yorta woman Tanya Day who was arrested for being drunk in a public place and died after hitting her head in a concrete cell at Castlemaine Police Station.
Her death was preventable, a coroner found.
Queensland is the only state that hasn't moved to decriminalise public intoxication.