The Frank Whittle Partnership (FWP) designed the ground.
Buckingham was contracted by the club in conjunction with FWP and will carry out build work on the 12,000 capacity stadium.
Scunthorpe United hopes to move into the new ground for the start of the 2016/17 season after been given the green light for development by North Lincolnshire Council.
The stadium is part of a plan for a out-of-town football and leisure development created by FWP on a site near the clubs present Glanford Park ground.
The ground will have club and executive facilities, a gym, office space and areas for commercial development as well as a club venue and supporters' bar.
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Plans by FWP also include a 100 bed hotel, a multi-use indoor arena, community sports pitches and a potential indoor/outdoor bowling facility.
A sweeping curve on the main stand designed by FWP is enhanced by a truss which pays homage to Scunthorpe's steelwork history.
Kevin Underwood, Partner/Director of Buckingham Group, said: "We are delighted to have secured this fantastic opportunity and are looking forward to work with the club and designers to deliver a superb stadium that the club and fans will be proud to call home."
Managing Partner at FWP, David Robinson, said: "We are delighted to be working with the Buckingham Group once again on this plan to create a vibrant and modern development that will be a real asset to the community and the local economy.
"The development at Scunthorpe aims to provide a real destination venue for sport, leisure and entertainment for the whole of the local community, with real benefits for the club and its supporters.
"It will provide the club and its fans with fantastic facilities and we've designed the stands to ensure the supporters are close to the action on the pitch, adding to the atmosphere and the match day experience.
"The plan will deliver a vibrant, modern new home for Scunthorpe United and its supporters and we can't wait to start work with the Buckingham Group on its construction."
(LM)
