Balfour Beatty was named preferred bidder for the project before the end of the year beating rivals Kier, Morrison and Robertson.
Final designs and costs are still to be agreed upon with the Scottish Prison Services ahead of a full construction start.
To be built on land to the south of Inverness Retail and Business Park, the prison would be the first building of its kind to be constructed in the Highlands for 112 years.
The proposed area of the building will be 123,000 sq ft including circulation, which represents an increase of over 66,000 sq ft from the existing prison facility. It will be built as a level 2 BIM project.
Delays in moving forward with the HMP Highland project since it was granted planning permission four years ago have seen costs rise.
The 2011 budget for the new prison was estimated at £52m, but it is now expected to cost anywhere from £98m to £110m.
The house blocks consist of a three-storey modern two-wing building with in-cell showering facilities and space provision for dining with circulation areas.