The group spearheading Assist (Advocacy, Support, Safety, Information and Services Together) say the pioneering project, which was launched in the city in 2004, could be used as a template when Scotland moves to a single police force next year.
As revealed in later editions of last night's Evening Times, Assist was rolled out across the Strathclyde Police force area after a £2.5million funding boost.
The project, which provides specialist support to victims of violence in the home, as well as calculating the risks involved, was previously only available to people living in Glasgow.
A total of 32 staff will now fill the roles across Strathclyde, which includes the city and surrounding areas of Lanarkshire, Dunbartonshire and Ayrshire.
The team members will work alongside divisional domestic abuse teams.
Since it was launched, Assist has helped to almost halve the rate of a victim being abused again, from 65% to 35%.
Strathclyde Chief Constable Campbell Corrigan said the force-wide expansion opened the door for Assist to be available to every person in the country.
He said: "If it can work in Strathclyde then it can work anywhere in Scotland.
"Anyone who doesn't think domestic abuse happens in other parts of Scotland is kidding themselves on.
"We've seen from our colleagues that they are very receptive to these models.
"I see this as an opportunity for every victim to get the same service.
"In a couple of years' time we'll hopefully be talking about the huge difference this has made. It has certainly thus far."
Mr Corrigan said he thought the country's most senior officer, former Strathclyde Chief Constable Steve House, would support the national roll-out of Assist.
He said: "I suspect that he would probably support the future for Assist, or a like organisation, right across the whole country."
Mhairi McGowan, head of service at Assist, which is based in the city's London Road, said that everyone in Scotland should have the access to the service being led in Glasgow.
She said: "What the Assist project has shown is that if you can talk to someone right after the incident and talk to them about the risk that they face then it is early intervention.
"If we can do that right across Scotland then I think it will make a difference.
"The new Scottish police force gives us a real opportunity that there will be no more boundaries, that no matter where you live your abuser won't be able to hide by moving from one force area to the next.
"I think it's a really good day for the victims of domestic abuse."
The funding has come from the Strathclyde Police Authority and the Scottish Government.
It is connected to a Scottish Government promise to give £34.5m in total to tackle violence against women over the next three years.
Glasgow Councillor Philip Bratt, convener of Strathclyde Police Authority, said he had a personal connection with the project.
He said: "It's something very, very important and it's quite dear to my heart. One of my cousins is a victim of domestic abuse.
"For me it was a no-brainer to add £1.8m into the budget because domestic abuse is a horrific crime."
He added: "I'd like to see the template we've developed here in Strathclyde rolled out across Scotland. It is something I will discuss at future meetings with the Scottish police authority, as well as the Chief Constable Steve House."
Glasgow's top cop said he hoped the funding boost would help to cut domestic abuse murders.
There have been four in Strathclyde so far this year.
Mr Corrigan said: "One of the things that's really important is the risk assessment programme that Assist specialise in.
"They understand who is the most vulnerable. It might be the alcohol, it might be a very chaotic life or other things they can identify through their professionalism – and those are the things that we will see murder reducing through, because Assist will identify people who are in those categories far quicker.
"It's complete tragedy.
"All murder is terrible but when I see it happening in this kind of band it is, dare I say it, even worse."