The firm is understood to have beaten regional rivals BAM, Wates and Kier to take the job for developer Cubex, which has been designed to achieve a BREEAM Outstanding rating.
Bristol City Council granted planning consent in September and work is now expected to start early in 2016 with the building due to be ready for businesses to move in by autumn 2017.
Cubex chose Willmott Dixon thanks to its track record at Colston Hall, Keynsham Town Hall and The Forum Building at Bristol and Bath Science Park.
John Boughton, operations director at Willmott Dixon said: “Aurora has been designed to a high specification that is rarely seen and we are delighted to be appointed as the preferred bidder on this landmark building.
“In line with the culture fostered by Bristol-based Cubex, we are committed to employing people from the surrounding local area and look forward bringing this building to life.”
Aurora is part of the Finzels Reach development, a mixture of commercial and residential properties with over 190 apartments sold to date and plans agreed for a 168 bedroom Premier Inn hotel and pedestrian bridge spanning Bristol’s historic Floating Harbour to Cabot Circus, expected to open in 2016.