The scheme, which has been designed with EPR Architects, will create nearly 3,000m 2of office space at the northern end of Blackfriars Bridge, and there are also plans for a new riverside café.
Owned by the charity the Bridge House Trust, the building will be cantilevered over the Blackfriars underpass and will vary in height between three to four storeys to protect views of St Paul's Cathedral.
The project has now been submitted for planning by the charity's sole trustee the Corporation of London.
Ted Hartill, the corporation's city surveyor, said: 'Bridge House will make an outstanding contribution to the urban fabric of Blackfriars, which is already home to a number of major employers, including Unilever and KPMG.
'The corporation intends to replace the existing building with this stunning scheme and attract a further major occupier,' he added.