It is phase two of a three-phase overhaul of the Oakwood Park buildings purchased by the college in 2012 from the University for the Creative Arts. Last December Denne completed the £13m first phase.
ISG has now been appointed to deliver new facilities for teaching construction and engineering, art, media studies and catering. It is scheduled to complete by July 2015.
Phase three will involve the building of a new commercial sports centre, also due in 2015.
MidKent College principal Sue McLeod said: “ISG’s record of delivering high quality results around the world speaks for itself, and we are confident they will meet our high expectations for this exciting project.”