There will be only 49 bespoke apartments in the exclusive Buchanan Gardens, which will be launched in April.
Bosses behind the one, two and three bedroom homes say interest has come from as far afield as Australia and Canada.
Prices of the flats, which will have a residents' roof garden and a gym, are not yet available.
Many of the apartments, which are being developed by Land Securities, will have private terraces and balconies overlooking the world-famous shopping street.
Estate agent Savills is selling the apartments and Jennifer Goldie, its head of residential development sales, said: "Never before have we seen this level of interest at such an early stage of development.
"A number of very well-known faces have shown an interest in buying one of the properties.
"The incredible location, high specification and unique design features mean there is likely to be fierce competition to snap them up."
The Buchanan Quarter residential and retail development was launched to transform a neglected site at the top of Buchanan Street.
The development will have the first Scottish branch of American fashion giant Forever 21, shoe shops Sketchers and Office. Fashion chains Gap and Fat Face, as well as Watches of Switzerland, are also confirmed retailers.
Work on the development is well under way, with the opening of the centre due on March 22.
The launch of the apartments is scheduled for April and the first residents are expected to move in a few months later.
Jan Eldridge, of Land Securities, said it was the firm's first residential development in Glasgow.
She said: "We have worked hard to make this one of the country's most innovative projects and all apartments are individually designed."
Scott Taylor, chief executive of Glasgow City Marketing Bureau, said: "Successful city centres thrive where people live in them.
"Opening up vacant spaces above and around our shops to residential use is a great idea and will help sustain local businesses. It has worked very well in the Merchant City already."