The car park at Ann Court will close permanently from midnight.
88 spaces will be lost as Andium Homes breaks ground for 165 new flats.
The States voted in January to release the £37.8m loan needed for work to start, after the Chief Minister put the project on hold last year.
Senator John Le Fondré wanted a new States HQ built there instead, but politicians voted 26-20 in favour of giving Andium the necessary funds.
Work is due to start tomorrow (5th March), and be completed at the end of 2021.