The business, founded by entrepreneur Paul Reynolds in 2010, has taken a 15-year lease on premises in the De Quincey building at the corner of Renfield Street and West Regent Street for its second outlet.
Mr Reynolds, who launched Cup with a shop on Byres Road in the West End which he says is making "good" profits, is planning with his new city centre branch to expand his offering from tea, cakes and lunches during the day to cocktails, wine, and desserts in the evening.
He declared that the De Quincey House outlet would be "Scotland's first dedicated dessert restaurant at night".
Mr Reynolds, a former executive of Marriott who left the hotels chain at the end of 2008 to undertake the charitable Saltire Foundation's one-year fellowship aimed at equipping people with the skills and attitude for a leadership role in Scottish business, said that 20 jobs would be created with the opening of the new shop.The entrepreneur, who owns Cup, employs 12 people at Byres Road.
He emphasised his continuing commitment to taking on apprentices, as he moves into the city centre.
Mr Reynolds plans to open his new outlet, in premises which he noted had been vacant for about two years and were occupied most recently by restaurant business Bouzy Rouge, during the third week in April.
He highlighted plans to offer tea, cakes, and lunches during the day before moving on in the
evening to offering cocktails based on Cup's own tea blends, wine, and a choice of between 20 and 30 desserts. The new outlet will be open from 10am to midnight.
Highlighting the fact that Cup's customer base continued to be mainly female, Mr Reynolds said: "Ninety-five per cent of our customers are female – that has not changed. It is just making sure we get that (offering) right for the city centre as well."
He added that the De Quincey premises were "perfect" for Cup, noting that their listed status meant the ground-floor interior of floor-to-ceiling tiles and chandeliers could not be changed in any case.
Mr Reynolds, who highlighted the fact that he was funding the expansion from internal cash generation without the need for bank borrowings, has already started work on the kitchen and toilet facilities in the basement.
He said that he had been in negotiations about leasing these city centre premises since December.
Mr Reynolds added that he had secured the lease on Tuesday last week.
He said of the move into the city centre: "It lets us expand into that evening market."
Noting that the Byres Road shop was at "capacity", he said that Cup was "turning away about 200 people on a Saturday".
He added that it was "heart-breaking" having to turn away customers.
Mr Reynolds said his business plan had always been to have two outlets in the one city, to "make sure scaleability is there", before expanding the business into other locations.
Although declining to disclose the current turnover of the Byres Road outlet, Mr Reynolds said: "It is still making good money at the moment.
"We are self-financing this (expansion). There is no borrowings."