Vinci will now develop detailed design with architect Sheppard Robson to allow the construction of a 13,500 sq m building at the Old Children’s Hospital Site, St Michael’s Hill.
Birse is in the last throes of site demolition and preparation under a separate contract before handing over to Vinci.
A project source said: “This is going to be a challenging job because its on quite a steeply sloping site which will make movement around the job more difficult.”
“Hopefully, Vinci will be able to start on site next month.”
The building will include research laboratories at one end with a central atrium separating teaching and administrative offices.
The Bristol project forms part of a more ambitious £80m plan to build a large university campus at the site, which will include a new mathematics faculty building.