The six-story government office block is set to be finished in July 2024, with civil servants moving in by the end of next summer.
Various departments will be moving into the new building on the site of the former Cyril Le Marquand House, leaving eight government buildings empty.
The plan is to either return those premises to their owners, or to use them for other purposes.
Some discussions are still going on about departments that will use the new space. However, it will house current Broad Street officials, and there are plans to move the Studio out of the Parade offices and into the new HQ.
Infrastructure Minister Deputy Tom Binet says having everything in the same place will make the government more efficient.
"It's going to bring various departments all under one roof from eight different buildings.
Most of it is preset as to who is coming here, but there is still some discussion about the other departments to make sure that the right people stay in the right places, and the right people come in to make it work properly.
It's a consolidation exercise basically, which I think most people accept as the sensible thing to do."
Infrastructure Minister Deputy Tom Binet, Assistant Minister Deputy Steve Ahier, St Helier Constable Simon Crowcoft and former Chief Minister John Le Fondre at a 'topping out' ceremony.
When asked about the total cost of the project, Deputy Binet told Channel 103:
"That is confidential information which I am not at liberty to impart."
Previously reported estimates have put the figure at between £90m and £130m pounds.
Government staff were moved out of Cyril Le Marquand in 2019 and into Broad Street temporarily - at cost of £1m a year - while Ministers considered a location for a single headquarters.
The previous administration chose demolition of the old offices and a return to the corner of Union Road and the Parade.
The former Chief Minister, John Le Fondré, said the move would save the government £7 million annually by reducing the number of offices from 21 to six.
The arrangement with developers Dandara, announced when demolition began in December 2021, was for a 99 lease of the States-owned land - with the government leasing the building for 25 years with an option to buy it outright at a pre-agreed price during the first three years.
Giving an update on progress at a 'topping out' ceremony to mark the installation of the final piece of the roof on the new building, Deputy Tom Binet, St Helier Constable Simon Crowcroft and the former Chief Minister John Le Fondré took turns to tighten a golden bolt.
A memory box is also going to be put in the basement of the new HQ, containing items, including a mug, contained in an old ammunition box donated by the Jersey Field Squadron.