The project, which has been dubbed the Scalpel because of its distinctive blade shape, was designed by Kohn Pedersen Fox for insurance giant W.R. Berkley Corporation.
The 190m tall building will have an internal floor area of 624,000 sq ft over 35 floors and two basement levels, including retail and restaurant areas.
Skanska is responsible for the construction, mechanical and electrical engineering and installation of services within the new development which is due to finish in 2017.