The firm has beaten-off competition from rival bidders Brookfield Multiplex, Bowmer & Kirkland and McLaren Construction to land the prized retail job.
The two-year revamp which will see a new roof, larger public areas and improvements to the surrounding infrastructure.
The plans, designed by Stirling Prize winning architects Stanton Williams, include a new 45,000 sq ft Harvey Nichols signature store and a three screen Everyman cinema.
Site owners Brockton Capital and partner Milligan Retail said the entire retail mall at The Mailbox will be enclosed and sky lit, to create an urban room with new facades, finishes and store frontages. Improved way-finding throughout the mixed-use scheme will be introduced.