Tashi Tahir, 17, and her mother Sharanee Bashir, 36, have been given permission by the Home Office to stay in the UK after 10 years of claiming asylum.
The family, who live in Knightswood, in the west of the city, were granted leave to remain after a long and drawn-out process.
Tashi, a pupil at St Thomas Aquinasm and her mother, who suffers from mental health problems, fled to the country from Pakistan because her mother believed their lives were in danger.
In March, this year, the family received a letter from Orchard and Shipman, the housing provider, which works on behalf of Serco and the Home Office, ordering them to pack up their belongings and be ready to leave in a matter of days.
Serco later said it was postponing the move until after Tashi finished her final school exams. She has now received a visa to stay here for two and a half years and will make another application after that.
Due to the positive developments she is also in talks with housing providers to arrange to stay in their flat.
She said: "It's changed things dramatically. Now we don't have the fear hanging over us that we might be sent home any day."
Tashi has been given unconditional offers at several universities - but has chosen to study maths at St Andrew's University where she has been offered a scholarship.
The gifted teenager is hoping to become an actuary.