Rye Demolition has finished clearing the Alie Street site which will be home to a 27-storey tower containing 235 apartments.
Barratt confirmed to the Enquirer that Getjar has won the concrete frame package continuing its long-standing relationship with the housbuilder.
Barratt will act as main contractor on the job and is currently tendering the curtain walling and facade package for Alie Street.
Five firms are in the running – Dobbler, Sipral, M Price, McMullen and Schneider.
A Barratt spokesman said: “We will be managing the job which is a very important project for us and is being developed in a joint venture with London & Quadrant.”