Prices for a one-bedroom flat in Buchanan Gardens will begin at £149,995, while the most expensive properties, which have three bedrooms, will cost £295,000 upwards.
Two-bedroom homes at the site, which is part of the city's new £70million retail and residential project Buchanan Quarter, will cost from £185,000.
The estate agent behind the sale says there has been "unprecedented" interest across the globe, with people from as far afield as India, China and Canada making inquiries, as well as famous Scots.
Bosses say more than 1000 parties have registered their interest in securing one of the 49 apartments, making it one of the most sought after sites in the city.
Most of the homes will have their own private terraces and balconies overlooking the centre of the city, while owners will also have access to a residents' gym, lounge and a sky garden.
Calum Miller, acting residential development sales manager at Savills, which is selling the flats, said: "Buchanan Gardens is proving to be one of the most popular developments we have ever worked on in Glasgow.
"With an unprecedented level of interest from local buyers as well as those from abroad, we are delighted this set of properties has caused such a stir in the housing market."
A show apartment will open next month.
Mr Miller said: "We look forward to our preview weekend later this spring."
The project was launched by developer Land Securities to transform the neglected site at the top of Glasgow's main shopping street.
Nine shop units are being unveiled as part of the site, creating more than 200 jobs.
American fashion firm Forever 21, Vans, Gap, Paperchase, Watches of Switzerland, Fat Face, Skechers and Office are expected to open on March 22.
Jan Eldridge, residential sales and marketing manager for Land Securities, said: "The volume of interest in Buchanan Gardens is astonishing, particularly as this is our first residential development in Glasgow.
"This is an innovative project that we have taken great pride in.
"Each of the apartments within the development is bespoke in its tailoring and specification and has been priced accordingly.
"We look forward to the official launch of the development."