The project is the latest in a series of builds, which have seen Kier and Willmott Dixon secure big projects, like its new library building.
R G Carter is understood to have beaten Kier and Morgan Sindall with a bid of £23m for the project.
Under present plans the project will involve demolition, refurbishment and construction works for the 60,000 sq ft block which amounts to a total investment of around £40m for the university.
The STEM building would give the university room to offer new courses in pharmacy, nutrition, physics, biochemistry, chemistry, geology and mechanical engineering.
A new substation will be located within the main car park of the University and an adjacent building re-clad in a dark grey coloured fibre cement panel as part of the project.
Vice chancellor Bill Rammell said: “The new STEM building marks the culmination of a huge investment at the campus, with the aim to give our students the very best learning teaching experience possible.”