Main construction work will start early in January after Miller fought-off competition from Morgan Sindall and Morrison.
Morgan Sindall is currently on-site completing ground clearance and infrastructure works under a separate contract.
The college is moving from the Longman in Inverness to a new campus on the outskirts of the city.
John Spencer, principal and chief executive of Inverness College UHI said: “We are certain the project will create many local construction jobs to boost the Highland economy.
“We expect completion to be in time for the start of the 2015 term.
“We are extremely excited to have a new purpose-built state of the art facility which will not only reflect the work of our students and staff but will also provide a superb student experience.”
Chris Webster, chief Executive of Miller Construction, said: “Our teams worked extremely hard on local employment initiatives and community benefits and we look forward to delivering these as part of this prestigious project.”