BAM will deliver the 13,000 sq m new building for Abertawe Bro Mogannwg University Health Board.
The three-storey extension will house renal dialysis, dental and x-ray departments as well as housing an education centre to train Health Board staff including post and undergraduate doctors.
The scheme is aimed towards a BREEAM Excellent rating, with features including photovoltaic cells on the roof, use of combined heat and power and modular services installation.
Completion is scheduled for autumn 2014.
Project manager Andrew Cavil said: “Not only will this scheme provide better facilities for patients, it will deliver improved facilities for the training of doctors, as well as creating job opportunities and boosting the local economy.”
The Morriston scheme was procured via the Welsh Health Estate Designed for Life Framework.
BAM has completed over £300 million of projects under the Framework, representing around 40% of the awards.