Dunedin Mayor Jules Radich confirmed yesterday Maria Dew, KC, had completed her investigation of Ms Graham’s conduct.
"The CEO has apologised to a staff member and the matter has now been concluded," the mayor said in a statement.
"I have full confidence in Ms Graham, who is continuing to focus on leading the organisation and developing the draft nine-year plan with the council," Mr Radich said.
"The matter is now closed and I will not be making any further comment."
The Otago Daily Times revealed in May the conduct of a senior manager at the council was being investigated.
In June, the council refused to disclose the terms of reference and said it "neither confirms nor denies the existence or non-existence of information asked for about a claimed investigation".
Ms Graham could not be reached for comment yesterday.
Councillor Mandy Mayhem said she would like to see the report and Ms Graham’s apology.
The council has yet to disclose the cost of the investigation and what its findings were.
Ms Graham has a five-year contract with the council.
It is due to end or be renewed in October next year.