The striking 13,500 square meter building has been designed by architects Sheppard Robson and construction is due for completion by the end of 2013.
Birse has now cleared the site under a separate preparation and demolition contract.
Patrick Finch, Bursar at the University of Bristol, said: “After many years of planning and preparation, I am delighted that we have now reached the stage where a construction contract for the Bristol Life Sciences building has been signed.
“We have great confidence that Vinci Construction UK, working closely with our project managers and designers and the Estates Office Capital Projects team, will be able to deliver an outstanding result for the University.”
Andrew Ridley-Barker, Managing Director of Vinci Construction UK, added: “We have vast experience in building top quality educational establishments and take great pride in delivering both buildings and surroundings that will enhance the research and learning experience.”