The Scottish Prison Service is client for the project, which is at Cornton Vale in Stirling.
The contract will involve the redevelopment of the existing facility in a phased programme of demolition and new build.
The first phase will provide two new residential blocks and a separate assessment centre. In addition, Morrison will build a new central hub with vocational and educational facilities, medical centre and laundry along with a family and visitor area and administrative building.
Phase two will involve the creation of a retreat and multi-faith area and an animal welfare and grounds maintenance building. The second phase will also include a new car park with EV charging points.
Bill Hocking, chief executive of Morrison’s parent company Galliford Try, said: “Morrison Construction continues to lead the way as contractor of choice for the public sector in Scotland and remains pivotal to delivering our strategy for the business.”