The contractor built the original 800-place prison between 1999 and 2001.
This latest contract involves building a 260-cell houseblock, together with a two-storey activity building within an increased secure site area.
Work includes the expansion and refurbishment of existing buildings as well as the construction of two five-a-side football pitches.
Skanska's professional team for this project includes Capita as lead architect, HBS providing mechanical and electrical engineering expertise and Watermans to coordinate health and safety during the design and construction phases.
Construction will begin in February 2008 with completion set for early 2010.