Audit Scotland is to study details of the 130,000 payment made to John Lindsay, the departing chief executive of East Lothian Council, on top of a 200,000 pension package.
The payments, which were agreed by the Labour-controlled council, prompted complaints to the Accounts Commission - the statutory body that oversees local government - because Mr Lindsay himself recommended the redundancy plan to the authority.
Until now, Audit Scotland, which examines councils' finances on behalf of the commission, had not made clear how seriously it would take complaints about East Lothian. But Caroline Gardner, the deputy auditor general and controller of audit, has now said there was no doubt it had the powers to investigate, even if there had been no complaint.
She said: "To clarify, the Accounts Commission and Audit Scotland are able to look at any matters which may seem relevant to the audit.
"There is no need to wait for a complaint to be received, and we are currently investigating the situation at East Lothian Council."
A spokeswoman for Audit Scotland said that investigations would be part of the annual audit of the local authority and the watchdog would also look at whether the deal provided good value for council tax payers' money.
However, the results of the investigation will not emerge until well after next week's local government elections, when most of the councillors responsible will have stood down, many with pay-offs funded by council tax payer.
Last night, David Berry, the sole SNP councillor on the outgoing East Lothian Council who raised the matter with the Accounts Commission, welcomed the investigation.
He said: "I would have been deeply disturbed had Audit Scotland not considered this a proper subject for investigation.
"I did not raise this matter lightly, as I realise it may appear politically motivated this close to a key election. However, my patience has been strained by a cavalier attitude of East Lothian Council's administration over eight years as councillor to the point that this was the last straw.
"What I find most perplexing is that the entire process will be complete - the outgoing chief executive retired, incoming chief executive installed and those who took the decision long gone with their severance payments - before any response can be expected."
Mr Berry, who is seeking re-election, defended his actions, which have been condemned by the Labour leadership of the council and the Tory opposition group, which backed the redundancy package.
He said: "If I have goal in this, it is to repair people's faith in their system of local government and its civic probity. I, and many people whose door I've chapped, see this issue as having damaged the council unnecessarily."
Stuart Currie, a Liberal Democrat candidate for the council, also welcomed the investigation.
He said: "I am glad that the disgraceful decision by the Labour-controlled council to make the chief executive redundant is being investigated. The redundancy payment to Mr Lindsay should not be made until such times as the new council has had the opportunity to study the outcome of the investigation and, in light of that report, revisit the original decision."
A spokesman for East Lothian said: "This decision was taken by the council as an efficiency drive and we are confident any investigation will confirm that."
Norman Murray, the former Labour leader of the authority who took a 20,000 "golden goodbye" after standing down as a councillor to seek election to Holyrood in Musselburgh East, said earlier this year that the decision had been taken by politicians, not Mr Lindsay.
However, the paper sent to councillors proposing the policy clearly stated it was from the chief executive.