Selected ahead of Allies and Morrison, Corrigan & Soundy & Kilaiditi and Berman Guedes Stretton, the practice has been asked to draw up a new masterplan for the town centre site, parts of which date back to the 15th century.
The building will house an interpretation and education centre on the ground floor, with a library on the first floor and an observatory above.
Etched in to the facade of the centre, which will be built from hand-made bricks and stone, will be a number of Shakespearian quotes including 'Better a witty fool than a foolish wit.'
The practice is also hoping to overhaul a handful of unsuccessful 1970s buildings which are considered 'detrimental to the overall experience of attending and visiting the school'.
Wright & Wright to redesign Shakespeare's school - images