Councillors had previously set aside £1m to convert the former Holy Trinity School into ten homeless units.
The investment is aimed at cutting the cost of placing homeless families into bed and breakfast accommodation.
The area currently has 70 families, including about 100 children, living in temporary accommodation, at a cost of more than £500 per place a week. The hostel, at the former school in Stirling, will open in the autumn. SNP councillor Alasdair MacPherson said: “Nearly 800 people have approached the council for help because of homelessness since April last year.
“By the end of February there were 250 homeless households waiting to be re-housed.”
He added: “This new investment in the service will go a long way to ensure that homeless applicants receive the quality of service they need when faced with a housing crisis.”