Torbrae Care Home in Castlemilk, which cares for people suffering from dementia, had recently been slammed by authorities.
The decision came after owners admitted they could not make the improvements "demanded by commissioners and the Care Inspectorate".
It is understood residents' relatives were told of the move last night.
The Evening Times last year told how an inspection of the care home led authorities to issue Torbrae with a formal improvement notice.
A spokeswoman for the home said: "Although this has not been an easy decision to make, we are convinced that it is the right one.
"It has not proved possible to make the sustained improvements that we ourselves expect, and that are demanded by commissioners and the Care Inspectorate.
"We will be working with residents, their relatives and all agencies to help find alternative homes with as little disruption as possible.
An improvement notice can be served when there are "sufficient concerns" about a home.
Previously, we revealed a nurse who was working at Torbrae Care Home was struck off. Stephen McMahon assaulted three vulnerable patients in his care, including a 98-year-old woman.
A spokesman said the incidents took place "under the home's previous ownership".