Balfour Beatty has already started work, with the project scheduled for completion in 2020. At construction peak, the project will employ a workforce of 250.
Building information modelling is being used to generate and manage information on site and minimise local disruption.
Dean Banks, chief executive of Balfour Beatty UK Construction Services, said: ““Our selection to this project builds on our vast wealth of experience in delivering significant developments across the UK, including the No.1 Palace Street residential scheme overlooking Buckingham Palace.
“We look forward to continuing our work with Brockton Capital over the coming years, successfully delivering a new first-class residence and its associated facilities.”