BAM was selected through the Procure 22 framework for the £30m development in Treliske.
Work on the main building phase will commence on site shortly after initial enabling works were completed at the end of January.
Key subcontractors for the job include T Clarke, WBM groundworks and Luscombes.
The new three-storey building, which will be an extension to the existing Trelawny Wing, is due to complete by autumn 2022.
Graham Kingdon, Construction Director, said: “We’ve been on site conducting minor works for the Trust over the last couple of years so we have formed a good understanding and relationship with them and our partners in advance of the major works commencing.
“We will have to keep the hospital fully functional during this time despite the technical challenges.”
The NHS Trust client team includes architect Stride Treglown, structural engineers Arup and mechanical & electrical designer Hoare Lea.