The project will be the first major construction scheme at Trinity College for 50 years.
Gilbert-Ash will construct 45 new en-suite study bedrooms, five dedicated teaching rooms, three multi-purpose areas for music practice rooms, additional teaching rooms and a basement for plant and storage.
The new Levine Building has been designed by Adam Architecture in a classical manner with traditional materials to reflect the established architectural character elsewhere in the college.
Raymond Gilroy, Gilbert-Ash Construction Director, said: “We are excited about the new building and what it will offer to the university community.
“We are in no doubt about the challenges which lie ahead, working in a tight location surrounded by listed buildings and grounds, but our team has the experience to meticulously plan for and work through any challenges which present themselves.
“We are ready to roll up our sleeves and work with our partners to deliver this prestigious project.”
Demolition specialist Erith is currently clearing the site with Gilbert Ash due to start main construction work next month and finish the scheme in 2021.