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.
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