The contractor will build the 4,500-square-metre administration block through the Designed For Life Welsh health framework.
It takes the total value of BAM work at the hospital close to £80m after previous projects to improve infrastructure; extend and refurbish a specialist rehab centre; and add a three-storey extension.
The ground floor of the new building will house some clinical examination rooms, while the rest of the building will be consultation offices and open-plan administration space.
The scheme will allow the hospital to consolidate all administrative roles in one place, freeing up rooms throughout the hospital for patient treatment.
Final decisions on the site of the block within the Morriston Hospital site, and the shape of the final building, have not yet been taken.
BAM project manager Justin Price said: “We are delighted to be continuing our important work on Morriston Hospital in Swansea. The project helps provide more continuity for our established local suppliers, extending our hard work to make sure our work benefits the local community, economy and environment as well as staff and patients at the hospital.”
BAM expects to start on site in January 2014 and to complete the project within 12 months.
Project architect is Stantec, with whom BAM worked on the Octav Botnar Wing for Great Ormond Street Hospital.
BAM is already at work on the £37m Phase 1b Health Vision Swansea project, which started in September 2012.
BAM’s work under Welsh Health framework has previously seen it deliver several other major healthcare schemes in South Wales, including the giant £128m Ysbyty Ystrad Fawr (Caerphilly General Hospital) after a 161 week construction programme.