It will be built next to Potteries Way and forms part of the wider Smithfield development, a £300m joint venture between developer Genr8 and Stoke-on-Trent City Council to create a new mixed-use district in the city.
The work will be completed in summer 2022 and is being funded by the city council, which will be responsible for operating it when completed.
This latest project in Stoke follows the Hilton Garden Inn Hotel and the neighbouring Clayworks apartments, also built by Willmott Dixon, which opened on the Smithfield site in 2020.
Willmott Dixon has extensive pedigree in delivering car park superstructures.
In the summer of 2020, the company handed over the 1,450 space Kings Dock Car Park to Liverpool City Council, creating the largest car parking structure in the city.
The business has also been contracted by Gateshead Council to deliver a £22.9m 1,000 space multi-storey car park in the Baltic Quarter of Gateshead, as part of an extensive regeneration of the area.