The birds of prey became surprise tenants after nesting on the 24th floor of the 27-storey building at 10-30 Petershill Court.
The empty building is due to be demolished by Glasgow Housing Association (GHA) and the first block was demolished in June this year.
To avoid illegally disturbing the nesting birds, GHA and its demolition contractors Safedem funded a new purpose-built nesting box at a nearby block of flats.
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Despite their efforts and those of RSPB Scotland and the Central Scotland Raptor Study Group, the adult peregrines stuck to their original nest and laid two eggs there in spring.
One egg fell at an early stage, but the pair raised a single chick, which left the nest on July 12.
The whole family is expected to leave the area in 3-7 weeks, when the chick can hunt alone.
Resident Steven McGrath first spotted the birds late last year.
He said: "I was concerned the birds might be at risk, so I decided to contact RSPB Scotland and others for advice.
"I've never heard of these birds breeding in Glasgow so I wanted to do everything I could to make sure they were successful."
David Fletcher of GHA joked: "Hopefully other peregrines will hear how GHA is such a great landlord and start flocking to Glasgow in increasing numbers."
And James Leonard, of the Central Scotland Raptor Study Group, said the project proved "industry and rare breeding birds can coexist".
Changing landscapes have pushed peregrines out of the countryside, their traditional habitat.
(NE/GK)
