The firm is believed to have beaten off competition from Balfour Beatty, Wates, BAM, Clugston, Bowmer & Kirkland, GB Building and Morgan Sindall.
Developer Wykeland Group has secured a host of major retail names including Arcadia, H & M, Wilkinson, Premier Inn and the anchor tenant Debenhams.
Thethe 10-acre development is due to be open to the public by Christmas 2015.
Other features include a five-screen digital cinema complex operated by Parkway Cinemas and multi-storey parking for more than 550 cars.
Dominic Gibbons, managing director of the Wykeland Group, said: “We believe Flemingate, by focusing on larger, quality national brands, will considerably broaden the town’s retail offering, making Beverley a top location.
“With Arcadia’s commitment to Flemingate coinciding with work commencing on site, we have reached a significant milestone in the development’s history.”
Willmott Dixon’s managing director in the North, Anthony Dillon, said: “Flemingate is a fantastic scheme for the whole region, attracting inward investment that will bring long-term economic and leisure benefits to Beverley.
“We have a strong track-record in the county and are looking forward to delivering a truly great shopping and leisure facility.”