Work starts in June and is scheduled to complete in August 2013.
The project will create new facilities with 14 en-suite single rooms and two triple occupancy rooms, maintaining the hospice’s capacity to care for 20 inpatients.
Hospice chief executive Peter Hartland said: “Interserve offered us best value plus commitment to a high quality process and product.”
Interserve divisional director Kevin Frain said: “As a native of the city, I have always been very aware of St Luke's Hospice and greatly admired its work. We at Interserve will be very proud to play our part in providing these excellent new facilities."