Construction is due to start this month and is planned to complete in autumn 2017, when the College celebrates being at the heart of the town for 150 years.
The four-storey sports block will include a 25-m pool, sports hall, dining facilities and link to a new three-storey, 32-classroom block.
A new sports pavilion will command views across the cricket and rugby field, with the development landscaping, complementing the listed flint boundary walls.
Key to securing the contract were the alternative methods of construction proposed.
Use of Silka large format blocks to the classroom block has provided cost and programme benefits, which will enable the building to be handed over in November 2016, a key requirement of the College.