The firm, part of Galliford Try, beat off bids from rivals Balfour Beatty, HBG and Kier to win the scheme for client Capital Shopping Centres. HBG is understood to have come second. The four tendered for the scheme last November.
The scheme, designed by retail practice Lesley Jones Architects, involves the refurbishment of every level, including work on floors, ceiling and escalators. The work will be phased to cut disruption. QS is Gardiner & Theobald.
Work is due to start on the 18-month project in the autumn. The shopping centre, opened in 1990, was originally built by Kier in a £200m deal. Until the construction of Bluewater in Kent, Lakeside was the largest out-of-town shopping centre in Europe.