The practice's victory will see the London firm redesign the university's humanities campus.
AHMM is proposing to strip the old buildings back to their frames, cut sections out of them and add new structures.
The altered buildings will then be given a new 'skin' which will add colours and patterns, in accordance to the buildings' orientation and function.
Practice partner Simon Allford said: 'The design is predicated on a series of moves involving cutting away and rewrapping.
'We are not wasting useful resources - rather reusing what is there to make a series of distinct spaces, which over the life of the new building can be occupied in different ways as the university develops new ways of teaching and learning.'