The scheme will see the original art deco frontage on Renfield Street restored and an 11-storey office tower built in what is a rundown part of the city centre.
"The planning consent is the culmination of our four-year commitment to developing an exciting addition to the urban landscape," said Bruce Hare, chief executive of developer Duddingston House Properties.
"In the past 18 months, we have liaised closely with both the council and Historic Scotland to develop a mutually acceptable solution. Our team has created an outstanding solution for this prime city centre site."
