The Oxford-based practice beat bids from Rick Mather Architects, MacCormac Jamieson Prichard and van Heyningen and Haward to land the job on the prestigious university site.
The winning scheme will boast a double-height theatre foyer, glass gable ends and a steel and timber roof which will 'hover' over the hall.
Explaining the design, a spokesman for the practice said: '[Our] vision was of the audience sitting in the garden, enclosed by ancient high stone walls with uninterrupted views to the fine surrounding trees.
'Seating and ancillary accommodation are conceived as a single piece of oak furniture sitting free of the enclosing envelope.'
There are also plans to redesign the garden next to the hall.
The practice is currently seeking listed planning consent for the project, which sits within the existing college - described by Pevsner as 'the grandest piece of Classical architecture in Oxford'.
A planning application is expected to be submitted in the summer next year and work is due to start on site in 2007.