The redevelopment plans will see the grade II listed front of the building retained on Lincoln’s Inn Fields.
The remaining rear building, which was built in the 1950s after catastrophic bomb damage during the Second World War, will be demolished and replaced with modern offices and teaching accommodation.
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Construction is programmed to start in early 2018 with the project due to be completed in 2020.
Wates will construct a new two-level basement that is deeper than the existing with a six storey concrete structural frame above.
The building designed by architect Hawkins\Brown will provide a new entrance on Portugal Street featuring a naturally lit new central stairwell.
The site is currently occupied by the RCS who will decant to the adjacent Nuffield Building for the duration of the building works.