It is part of an £80million plan to build five care homes across the city that will accommodate 600 elderly people.
The package will also include the construction of four day-care centres.
Sites have been identified for four of the care homes, with work on one being built in Bardowie Street, in the north of the city, having started this year.
The council has now concluded a deal with NHS Greater Glasgow and Clyde that will result in a new care home on the Knightswood hospital site.
It involves the NHS swapping the land for five smaller parcels of land belonging to the council.
Health bosses hope to use the five sites for a range of new community-based health facilities.
All five new council care homes will have full en-suite facilities in all bedrooms and a range of communal spaces with easy access to outdoor spaces and gardens.
Liz Cameron, the council's spokeswoman for development and regeneration, said: "We are delighted to have reached agreement with the NHS over the Blawarthill site following long and detailed negotiations.
"Once the site became available, it was quickly seen as the obvious location for the council's new care home in west Glasgow.
"A care service has been provided at Blawarthill for generations and I am very pleased this decision will help that continue.
"Residents in the surrounding communities of Knightswood and Yoker were very determined to see a first class care centre on the site and I am sure they will be very pleased with the home once it is completed.
"It will be innovative and greatly enhance the quality of care available to vulnerable, older people in the area.
"This deal represents great news for west Glasgow and the city as a whole."
The land involved in the swap for Blawarthill includes the former site of Gairbraid Primary, Maryhill; a site at Cleland Street and Gorbals Street; and the site of a former social work office in Garscube Road, Firhill.
It is also expected health board bosses will dovetail their plans for local health facilities with continuing developments at sites in McCulloch Street, Pollokshields, and Saracen Street, Possil.