The contractor beat off competition from rivals Thomas Vale, Interserve and Willmott Dixon to bag the job.
The development has been designed by Associated Architects and is known as the SPACE building (short for Sports and Performing Arts Centre).
It will include a four court multi-use sports hall and fitness facilities for school and community use, as well as dance and drama studios, teaching spaces and a VI form centre.
SPACE marks Associated Architects’ ninth project for the King’s School Worcester, including the recently completed Michael Baker Boathouse, which has been shortlisted for a RIBA award.
Associated Architects director Matthew Goer said: “We’re looking forward to working with Kier, to deliver a high quality building for The King’s School Worcester.”
The project is due to be completed Summer 2014.