Work will start on site later next month to construct the contemporary designed expansion of the current school.
The new building will include new teaching, staff and visitor facilities, across two wings of accommodation separated by a metal clad drum that forms a curved atrium.
The accommodation includes open plan office space, an undergraduate suite, post-graduate teaching spaces and a behavioural laboratory.
B&K is believed to have fought-off competition from BAM, Wilmott Dixon and Kingerlee to land the deal.
Graham Hall of Associated Architects, said: “Bowmer and Kirkland provided an impressive tender submission and saw off stiff competition from three other contractors.
“We’re looking forward to commencing on site and delivering this first class teaching building for the University with Bowmer and Kirkland.”