The firm has beaten off rivals Sir Robert McAlpine, which has recently successfully bid a raft of work, Balfour and Laing O’Rourke.
Construction of the 400,000 sq ft building is expected to start in August at the site of the former national hockey stadium.
BAM Construction won a pre-construction services agreement last December to assist in the second stage of the design and procurement process.
When complete in 2012, it will house up to 3,000 staff and be one of the most sustainable in buildings in Britain.
It includes a host of eco-friendly features including extensive ‘living roofs’ and a rainwater harvesting system that will be used to flush toilets and irrigate landscaping.