The group has bought the freehold on the restaurant from Baronsgate Estates for around £700,000 to become owner and operator.
The iconic restaurant at 652 Argyle Street started life as a merchant's pub in 1856 and was established as a restaurant 100 years later under the Lamont family to become an icon of fine dining in the City.
Its popularity with the powerful local business community may have helped the building survive the general razing to the ground of the much of the Anderston district during the 1960s and 1970s.
The restaurant was relaunched in April 2002 under Ian Fleming, who acquired the leasehold for £275,000. He has now relinquished his interest to concentrate on his Lake hotel at Lake of Menteith.
The business, which covers the basement and ground floors of a tenement building, comprises the 50-seat main restaurant and the 30-seat Belfry restaurant.
Following a refurbishment, it will reopen in August as Two Fat Ladies at the Buttery under head chef David Monaghan.
The Buttery sale was the first deal to be clinched by Knight Frank's newest partner, David Reid.
By Angela Frewin