Contracts have been exchanged to build the new government headquarters on the site of Cyril Le Marquand House.
The developers will now prepare a planning application.
The Chief Minister, Senator John Le Fondré, has toured the old building before demolition work begins.
In a video published on the government's social media channels, he says the project has many benefits:
"It's going to free up much-needed space, mainly in St Helier, for housing or other purposes. It also means most services will then be in one place, and therefore much easier to access.
"So as well as reducing the government's literal footprint in town, it's also going to reduce our carbon footprint - being built to a higher environmental standard and helping us to environmental commitments.
Government of Jersey video
"The estimated financial benefits are also impressive, with revenue savings worth around £7million a year."
The Scrutiny Liaison Committee wanted to delay approval of the plans so they could be reviewed first, but that was rejected.
The building will be occupied for up to three years, during which there'll be an option to buy it at a pre-agreed price.
If that isn't taken, the government will enter into a 22-year lease instead.
Politician calls for Havre des Pas lido tender process to be scrapped
Two Jersey rowers make Team GB
Jersey's rate of inflation rises slightly over summer
Committee calls for Deputy Philip Ozouf's suspension
Baby sloth at Jersey Zoo orphaned as mother unexpectedly dies
DFDS contract reveals termination clause and performance penalties
French racing trimaran winched ashore off Guernsey
Ballet d’Jèrri returns to Opera House tonight
