Trenton Square will also be extended as part of the build process, which is expected to take around two years.
CEO Lee Henry said the public-backed States of Jersey Development Company (SOJDC) was in the “final stages of detailed negotiations” with the firm that will act as “anchor tenant.”
In preparation for enabling works to begin, the short-stay car park at The Esplanade will close permanently from Tuesday 5 October.

Pictured: SOJDC says the building will meet BREEAM standards, making it one of the most environmentally friendly builds in the Channel Islands.
SOJDC explained that it created a 520-space car park at Les Jardins in 2015 in advance as an eventual replacement for the Esplanade car park. The Esplanade remained open while further spaces were added to Sand Street.
Infrastructure Minister Deputy Kevin Lewis commented: “We know the nearby Sand Street carpark has spare capacity to accommodate regular users, and on Level Four of the carpark we will be putting in additional disabled parking, along with nine extra parent/child bays. We’ll also put extra disabled parking spaces at Les Jardins carpark, with additional motorcycle parking created on the Esplanade.”