The practice, commissioned by developer the Cathedral Group, will redevelop and extend part of the hall, designed by Sir Ernest George, to incorporate a new conference facility, as well as provide a new leisure club and spa.
The practice has also been asked to improve accessibility throughout the hall, as well as creating a 'stimulating and contemporary environment, while respecting the existing architecture'.
The architect was praised for its sensitive treatment of the new addition to the hall, with West Oxford Council saying that it harmonised well with the existing building.
Robert Parkinson, conservation manager for the council, said: 'I was very impressed by the way that the design team researched the history of the building and the park, and that background informed the design process. The architects have not been overawed by Sir Ernest George's work.'
Work has already started on the interior of the existing hall, with construction on the new project expected to commence in the summer.