The C. H. Smith site is likely to have new owners by the end of the month.
Developer Errol Stewart said he sold the site "pretty easily" for an undisclosed amount.
An interstate organisation from Melbourne has bought the whole site, except for the council-owned car park.
Mr Stewart expects the deal to settle when the state government signs its lease on the building.
"We have contracted it to sell. It's due to settle when the government sign their lease, but they haven't signed their lease," he said.
The money from the sale will be used to fund his next project. This includes a plan to build two residential towers across the road from Silo Hotel.
"If I go and build these towers I'll need some money and you can't keep absolutely everything," he said.
"We'll be able to build a bit more for Launceston, or Hobart, or a bit in the bank and take it easy."
The site was not advertised on the open market, with Mr Stewart saying there are lots of potential players in the market for sites like C. H. Smith.
"We really just spoke to our accounting firm who approached a couple of their major clients and said there is an asset ready for completion in 2019 and this is what it is and we sold it pretty easily."
Treasurer Peter Gutwein said the C. H. Smith lease included a rent-free period while the fit out works were completed.
"The occupation of the C. H. Smith building commenced with the Department of State Growth relocating during June," he said.
"The move into C. H. Smith has provided opportunity to consolidate our operations across Launceston and provide a more efficient utilisation at government occupied sites."
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Staff from Communities Tasmania, the Health Department, Human Services and the Education Department, as well as Service Tasmania will progressively occupy the building during July and August.
Henty House will continue to be fully occupied by government tenants once the consolidation is completed, Mr Gutwein said.
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