NHS North of England has given go-ahead for the two projects and agreed to send plans for a redeveloped £90m West Cumberland Hospital to the Treasury for final approval.
Robertson will start work on Phase 1 of the new Cockermouth Hospital in the early summer with completion expected in autumn 2013.
The same contractor will also start on the health centre in Cleator Moor in early summer which will be completed by the end of spring 2013.
Both developments are being delivered by eLift Cumbria, the development partner arm of NHS Cumbria and are is funded through the NHS Local Improvement Finance Trust (LIFT) programme.