Beard will enlarge the building by converting the basement space into offices and a conference centre
A central staircase will be installed inside the existing marble-clad rotunda, descending from the foyer to the new conference centre.
A glass structure will also be constructed at ground level above the new office space and carbon-fibre reinforcement added to provide support to the existing structure.
Rhodes House is home to the Rhodes Trust, which administers scholarships for overseas students to study at the University of Oxford.
With the bulk of the project involving works below ground level, it is anticipated that most of the Trust’s operations will continue as normal during construction.
Subject to planning consents it is hoped that the main construction will begin at the end of July 2020.
The project is expected to take approximately 24 months to complete, enabling the new facilities to open in autumn 2022.
Dean Averies, director for Beard Oxford, said: “This is a once-in-a-lifetime project. The Rhodes Trust is a world-renowned institution, and Rhodes House is a very special building in its own right. Our longstanding association with the University of Oxford means Beard is ideally placed to deliver facilities that will enhance the trust’s work while respecting the history of the building and the trust.”