Its Leeds office will build a 25m swimming pool, fitness and medical facilities to complement the existing tennis centre.
BAM is finishing off a major new leisure centre in nearby Huddersfield – and an estimated 80% of the supply chain by project value will come across to the Sheffield scheme.
The Graves Leisure Centre project broke ground last week, with completion scheduled for summer 2016. Photovoltaic cells and other renewable energy will be used to help the project meet sustainability aims.
BAM will also work with local suppliers, workers and the community on the project as part of the YORbuild framework.
BAM senior design manager Noel Banfield said: “We are very much looking forward to beginning on this important project, which will contribute to health and wellbeing in Sheffield and beyond.
“Building and testing swimming pools in particular is very technical and complex, so we are delighted to be bringing across much of the management and wider team from the Huddersfield scheme. This will bring huge efficiency benefits to the project to extend these facilities.”