The move by Scoban, headed by former Adam and Company managing director Ray Entwistle, signals definitive progress for the bank, which issued a fund-raising prospectus last March.
It had raised £5 million from private investors by the end of June, against a target of at least £8m to start up the bank, and pending discussions with the Financial Services Authority over a banking licence.
The lease has been agreed with The Charlotte Square Collection, launched by Corran Properties, which has secured control of some 19 properties in the square.
Nick Ball, director of Corran Properties, said: "This is a fine demonstration of our belief that creating buildings and public space of the highest quality will result in new investment in the city. We're grateful to Ray and his colleagues for supporting this vision."
Scoban will occupy 22 Charlotte Square as a temporary head office during the refurbishment programme and relocate to 9 Charlotte Square, until recently the headquarters of Sir David Murray's Murray International Holdings, on completion of the works.
Mr Entwistle said it was "an important stage in the formation of the new private bank".
He added: "We were particularly impressed with The Charlotte Square Collection's vision to restore the fortunes of Charlotte Square and we believe the planned improvements will attract new investors to the city, as well as clients for Scoban.
"Our overall plans for the launch of our new private bank are making good progress."
Scoban had originally hoped to launch the bank this year after a strong initial response from potential customers.
Mr Entwistle said: "We have now got 200 private shareholders who want us to set up a new private bank."
Shareholders at the bank's annual meeting early next month are likely to have to await news on the company's critical discussions with the FSA and with potential major investors.
The regulator has discretion to allow a provisional banking licence to be granted pending the raising of the £75m of capital needed for a full licence.
Mr Entwistle told shareholders earlier this year institutions had been unwilling to invest until a provisional licence had been secured, while "considerable interest has been shown in Scoban's strategy from large, well-established organisations".
The veteran banker said yesterday discussions were continuing with various parties and with the FSA.
He added: "We are very confident about the future but there are lots of different avenues being looked at very carefully.
"We raised our £5m by the end of June and we are still building our team. There is a clear understanding that quality of service is what we are all about."
The new bank is likely to stress its interest in private banking customers at all levels, as many of the big institutionally owned private banks are retreating to serve only ultra high net worth clients.
Mr Entwistle launched Scoban in January 2011. He told The Herald the project had attracted disillusioned bankers, and intended to train younger recruits as traditional bankers.