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She will take up the role after the July 17 departure of chief executive Sue Bidrose, who is leaving to head up AgResearch in Christchurch.
Ms Graham is general manager of City Services and she has held a range of senior positions at the council.
The appointment of an acting chief executive was confirmed by councillors at this week’s Dunedin City Council (DCC) meeting.
The recruitment process to find a permanent replacement for Dr Bidrose is also under way.
Ms Graham first worked for the DCC in the mid-1980s as a member of a roading crew.
She returned to the organisation in 2007 and her roles included Corporate Services group manager, and Strategy and Governance general manager. She has been City Services general manager since October 2018.
She is also the lead Dunedin Civil Defence controller.
The council's executive leadership team will have a temporary reshuffle.
Parks and Recreation group manager Robert West will fill in for Ms Graham as acting general manager of City Services. Parks and Cemetery manager Scott MacLean will cover for Mr West, also in an acting capacity.