The contract was signed off as the joint venture struck a deal with HSBC to provide £125m to fund the 8-storey 10 King William Street project.
McLaren has been working on the project under a preconstruction agreement, with Keltbray as enabling works contractor.
The 140,000 sq ft Bank scheme will be built above the new station entrance on Cannon Street and is designed to target the highest ESG credentials including BREEAM Outstanding, NABERS 5* and WELL Platinum.
The project team includes cost consultant Core Five, M&E consultant Hoare Lea and structural engineer Robert Bird.