The London-based practice saw off competition from Wilkinson Eyre, Rafael Viñoly, KPF and Dixon Jones to land the commission at Keble College.
The project is the latest Oxford success for the firm, which won the archive and library building for Queen's College, and a music room for Corpus Christi College.
The Keble project will see the construction of a large new building on a 0.7ha former hospital site extending from Banbury Road to Woodstock Road in the city centre.
The development will be made up of residential, communal, teaching and research facilities in a single complex.
Keble's bursar Roger Boden said the college was pleased to reappoint the practice after previous successes.
'Rick Mather Architects has already designed two award-winning buildings for Keble, of which we are very proud,' he said. 'However, we felt that for such an important project it was essential to have an open competition.
'That process took five months and resulted in five very strong and very different final proposals. We spent over a month evaluating these and in the event the jury panel of 10 was unanimous in its choice.
'The winning proposal offers a 21st-century reinterpretation of the traditional Oxford quad that meets or exceeds all elements of the brief,' Boden added.