The Grid will provide 277,500 sq ft of Grade A space over 12 levels designed by local architect Cooper Cromar.
Demolition of the existing building is planned for later this year with construction completion scheduled for late 2021.
William Badger, Asset Manager at M&G Real Estate, said: “With a lack of new Grade A space in the city’s office market, as well as in nearby Edinburgh, we are confident that The Grid will attract strong interest.”