The 120,000 sq ft campus will be built in Sunderland city centre on the land known as the Holmeside Triangle opposite Park Lane bus station.
It will be delivered in two phases and will accommodate up to 2,000 students on courses include engineering, manufacturing, construction trades, automotive skills, travel and tourism, catering and hospitality.
BAM is understood to have beaten rivals Bowmer & Kirkland, Sir Robert McAlpine, Shepherd and Willmott Dixon to the deal, which is still in the standstill period before award.
The college was one of the big winners when the Department for Business, Innovation and Skills announced grants of £194m nationwide to improve further education colleges.
Sunderland is to receive £10m, which will be added to funding for the new development from the city council and college reserves.
Sunderland-based DESCO (Design & Consultancy) is the mechanical and electrical consultant on the project with Turner & Townsend acting as cost consultants.