The firm will renovate and reconfigure the Grade II listed Radcliffe Science Library to create common rooms and study space for the new Reuben College.
Works also include the modernisation of the RSL on the top floor and the refurbishment of a two-level basement to serve as a high-quality storage and teaching facility for museum collections.
Construction work will begin imminently and complete in time for the new academic year in 2021.
James York, area director at Morgan Sindall Construction, said: “The RSL is steeped in history; both the building itself and the invaluable knowledge and records contained within its books, manuscripts and museum collections.
“Our work will ensure they can be preserved and displayed for years to come, while also serving as an inspiration to the next generation of post-graduate students studying in the first Oxbridge college to be established in three decades.