Designed by architects Stanton Williams, the project will feature a new 45,000ft² Harvey Nichols store and a three-screen, 12,000ft² Everyman cinema.
Brockton Capital is the principal owner of the Mailbox and Milligan is the joint-owner.
Galliford Try central managing director Sean Bowles said: "We look forward to working with our partners at Brockton Capital and Milligan to bring our expertise to bear and create facilities at The Mailbox that befit a luxury shopping experience and reflect the high-quality of the brands that will be based there."
Plans also include construction of a new roof, larger public areas and improvements to the surrounding infrastructure.
Pre-let agreements have also been signed with fashion brands Jaeger, Gieves & Hawkes, L.K. Bennett and Daniel Footwear.
Castle Fine Art will open a new gallery within the mixed-use scheme, which will feature a bar and food service.
The cinema is scheduled to open towards the end of 2014, while re-development of the Mailbox is expected to be completed in 2015.
Milligan development director Howard Penstone said the refurbishment will transform the environment of the building and bring a collection of brands to Birmingham.
"We’ll be working hard throughout the next 18 months to ensure that we stay open and luxurious, with a whole host of events and activities planned ahead of completion in 2015," Penstone said.