The most senior officials in Treasury, education and transport will each receive about $450,000 in payouts after the newly elected government showed them the door within weeks of taking power, adding further strain to the state's finances.
Mr Minns on Friday warned of deep issues with the NSW budget as his government worked to establish the exact debt position inherited from the previous leadership.
"We've detailed different aspects of education and transport over the last week but I have to tell you, and I in effect warn the people of NSW, there's much more to talk about when it comes to Treasury and the budget situation," he said.
"This is going to be certainly one of the most important agencies and decision-making places of the government over the next 12 months."
The previous government's forecasts anticipated debt would reach 13 per cent of the state's economy by June 2026.
Mr Minns declined to elaborate on exactly where the issues lie, saying treasurer Daniel Mookhey would speak further on the topic in the coming days.
As part of his plan for a fresh start for the state, the premier announced a string of changes to the public service including the reinstatement of a Cabinet Office to provide advice to his government.
Mr Minns said he planned to scrap the current "cluster" public service model in favour of a more top-down approach.
"I don't believe that the cluster model has enabled good decision-making over a long period of time," he said.
"It's pushing down decision-making theoretically at the departmental bureaucratic level, but in reality, there's no substitute for the Cabinet Office.
"My expectation is that all government departments will have a laser focus on serving the community."
The existing Department of Premier and Cabinet (DPC) will be dissolved from July 1 and replaced by the Cabinet Office and a new separate Premier's Department.
Both new agencies will report directly to the premier, a model Mr Minns said was used by the Greiner and Carr governments.
Treasury secretary Paul Grimes, education head Georgina Harrisson and transport tsar Rob Sharp are being offered the bumper payouts as the trio are contractually entitled to 38 weeks' pay of their $623,300 salaries.
"I want to sincerely thank these leaders for their service and dedication to the people of NSW," Mr Minns said.
Former treasurer Matt Kean lauded Dr Grimes as an intellectual pillar of the public service and "easily one of the best public servants" in Australia.
"In the best traditions of the public service, he always provided the highest quality frank and fearless advice. Paul's departure will be NSW's loss and someone else's gain," Mr Kean said.
Secretary of the current DPC, Michael Coutts-Trotter, will oversee the delivery of the Minns government's first budget in the coming months as acting Treasury secretary.
Mr Minns said he valued the experience and advice of Mr Coutts-Trotter, who is married to federal Labor minister Tanya Plibersek and led several departments under the previous coalition government.
Sydney Trains chief executive Howard Collins will step into the transport vacancy while senior education official Murat Dizdar and senior public servant Peter Duncan will take charge of the education department and DPC respectively.
Each secretary role will be advertised and openly recruited in coming months.
Further changes to the structure of the public service are being considered.
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