The two design and build jobs at its Digby Stuart College Campus site in south London are worth around £40m.
The new library will be around 70,000 sq ft, and will be the first phase of the expansion to be started on at the turn of the year.
Osborne has also won the contract to design and build around 400 new student bedrooms.
These will be arranged as self-contained flats, around student services accommodation and up to 150 basement or ground floor car parking spaces.