The practice saw off locally based practices Reiach & Hall and RMJM as well as international commercial giant KPF to land the project on the university's Little France campus.
The facility will house scientists carrying out cutting-edge stem-cell research.
According to the practice, the building's design has been inspired by stem cells' ability to 'transform into a variety of other tissue cells'.
The design statement reads: 'The nucleus of the scheme, the proposed central support area, acts as the stem cell which, via a series of connecting bridges - the arteries - converts into the functional laboratory buildings - the tissue.'
New laboratories will be built along two sides of the site, linked by a central hub building which will house write-up spaces, meeting areas and a library.
There are also plans for a new café overlooking a large water feature.
Included in the winning design team were structural and services engineer Buro Happold, planning supervisor Turner & Townsend and landscape architect Ian White Associates.
The development is expected to go in for planning next April.