Developer Intu is expected to commit to the project later this year allowing work to start on the big retail scheme in early 2018.
The planned revamp will involve demolition and reshaping of the centre while shops continue to trade.
Planning was obtained over 18 months ago for the scheme, which is expected to take two years to complete.
McAlpine secured the job after fending off bids from Laing O’Rourke and Bowmer & Kirkland.
It forms the key part of Nottingham City Councils £250m scheme to regenerate the Broadmarsh area of the city centre.
The Broadmarsh multi-storey car park and bus station next to the shopping centre will be redeveloped.
G F Tomlison has picked up the £25m project to rebuild the car park and bus station adding commercial units along both Collin Street and Carrington Street
Demolition work is expected to get underway shortly with the project due to be complete by autumn 2018.