The scheme is a refurbishment and remodelling of an existing 4250 m2 building, including an internal fit-out and M&E upgrades and installations.
The new building will provide incubation space for start-up businesses. It will also be home to the Bristol Robotics Laboratory.
BAM won the contract through the Construction Framework for the South West. Parsons Brinckerhoff is the architect.
Completion is scheduled for December 2016.
BAM construction director Craig Allen said: “We are delighted to have secured the new enterprise zone project with the University of the West of England. We look forward to building on existing relationships with the University having successfully delivered their new students union building earlier in the year. The Enterprise Zone will be a great place to do business for new firms which will create jobs and be boost to the local economy”
UWE pro vice-chancellor Martin Boddy said: “We are delighted to have BAM help us develop the first University Enterprise Zone supported by the government, just one of four in the country. Construction is now under way for this development on the Frenchay Campus which will provide significant support to the region’s innovation and business growth.”