It will demolish the Stand Cullis (North) Stand and replace it with a new two-tier stand.
The contractor is aiming to complete the lower terraces early next season to allow some uncovered seating to be released back to the club as soon as possible.
Project manager is Drivers Jonas Deloitte and architect is AFL.
Buckingham is also working on the £73.5m American Express Community Stadium in Brighton.
The contractor was also recently awarded a £6m design and build contract for a new head office for Domino’s Pizza Group in Milton Keynes.
As previously reported, planned later phases of the Molyneux redevelopment include rebuilding the Steve Bull (East) Stand in time for the start of the 2014/15 season and then rebuilding the Jack Harris (South) Stand.
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