But officials have cut the number of men to be offered accommodation and are to open it in a phased approach.
As reported by the Evening Times, the decision to use a former care home to house 40 homeless men has caused fury among local people.
Locals in Burnbank Gardens, which sits between Great Western Road and Maryhill Road, say it will create a danger for the many families, single women and elderly people in the area.
We can now reveal the plans will go ahead but £150,000 will be spent improving security at the site, including installing CCTV cameras.
Councillors spent more than an hour thrashing out the details of the proposals for the Burnbank House site in the City Chambers last night.
It was agreed to introduce the men to the area in a phased approach.
Initially, 25 men will be given accommodation at the West End home.
Council bosses will gradually increase that number to 35 then 40, if the home passes all the relevant independent tests.
A Glasgow City Council spokesman said: "We have listened to the concerns of the community and have taken on board the points they have raised.
"We have agreed to modify our plans so that a smaller number of people affected by homelessness will be initially accommodated at Burnbank.
"Subject to an independent assessment of how the home is run as a homeless facility, we hope to increase the capacity to 40 people on a phased basis.
"We will continue to engage with members of the community to provide information and assurances on how the home will operate in practice."
Council bosses stressed the hostel will be properly supervised by staff, with strong links to police and community safety services.
The homeless hostel plan will be implemented on October 1, according to Glasgow City Council.
Hillhead Councillor Martin McElroy previously called for adequate CCTV coverage at the home, new outdoor lighting and to its garden landscaped to ensure that there are no hidden spots.
He said locals are concerned about the number of men who will be in the unit and whether they will have a history of addiction, mental health issues or a criminal past.
Council approval came after campaigners handed over a 1100-signature petition demanding a halt to proposals for the centre, which is currently a care home for the elderly.