MD Derrick Jones left his job of two and a half years after the Association of Local Authority Chief Executives (Alace) negotiated a compromise agreement that included a year’s salary.
Alace secretary Alastair Robertson said an allegation had been made to the police that Mr Jones had been harassed by a councillor.
He said Mr Jones had neither complained nor believed himself to have suffered harassment.
North Wales Police confirmed that a complaint had been received “in relation to events within the council”.
Leader Phil Fowlie (Original Independents) thanked the outgoing chief “for his contribution to the authority”.
Mr Jones said: “I leave with a heavy heart and trust my personal efforts will be built upon and strengthened for the benefit of Anglesey.”
Anglesey’s turbulent internal politics are dominated by independent factions and a history of troubled relationships.
Alace was also involved when previous chief executive Geraint Edwards left in 2006.
Mr Robertson said: “Alace has had to be involved with the departures of both the current and previous chief executives because of the exceptionally challenging political arrangements.”