Longstone, who makes around $660,000 a year, was appointed in July last year on a five-year contract.
The new head of Work and Income, American Janet Grossman, is in line for a similar relocation payment.
Briton Gabriel Makhlouf was appointed head of Treasury last year. Two other Government departments, the Inland Revenue, and Economic Development Ministry, have longstanding chief executives from overseas.
Labour state services spokesman Chris Hipkins said the amounts were worrying "when we should be able to fill these positions ourselves."
The Herald on Sunday requested a response from acting State Services Minister Tony Ryall. Present minister Jonathan Coleman was out of the country.
Ryall's office referred questions back to the State Services Commission, whose spokeswoman Marian Mortensen said: "He has not got the time to speak to you."
She said relocation fees were an "operational matter" which did not concern the minister.
On its website, State Services boss Iain Rennie says: "Chief executive vacancies are widely advertised. While the majority of chief executives are New Zealanders or have a New Zealand background, the search can extend overseas in order to reach the broadest range of talent."
In a statement, the State Services Commission said the amount paid in relocation fees was an estimate of the cost of moving to New Zealand.
"This estimate is calculated on the basis of knowledge of previous relocation costs, and other information obtained for this purpose."
Under their contracts, chief executives would have to repay the amount if they leave the job within a year.
The Herald on Sunday fought for a year to reveal the relocation payments.
Chief Ombudsman Beverley Wakem said: "It is generally accepted that the public interest in accountability for public expenditure is high. Consequently, this public interest may need to be recognised by release of sufficient information to satisfy that public interest consideration."