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Prof Hayne, who has led the university since 2011, will finish in April next year and start as vice-chancellor at Curtin University in Perth, Western Australia, later that month.
Saying goodbye would be hard, but she was looking forward to her new adventure, she said.
“What started as an academic adventure here at Otago turned into a career that has been second to none," Prof Hayne said.
"I will leave Dunedin with a heart full of great memories of the students, staff and alumni who have been such a huge part of my life here.
“Over the course of my time as vice-chancellor, I have had the opportunity to meet so many people who received their start at Otago and who met friends they have kept for a lifetime.
"The living-and-learning environment that we have created here over the last 151 years continues to leave its mark on the students who are lucky enough to study here. The university has also left its mark on me.”
Professor Hayne said her time at Otago had been enriched by the students she had met.
“Students always have been the lifeblood of the University of Otago and they are the main reason that I get up and come to work every morning.
“I am particularly grateful to my own postgraduate students who have been a constant reminder of what a university is all about.”
The university’s first female vice-chancellor, Prof Hayne took on the role in 2011 and her five-year contract was extended five years in 2016.
University of Otago chancellor Royden Somerville said Prof Hayne had been an outstanding leader at the university and ensured it was well positioned to confront the challenges of the 21st century.
A highlight of her tenure was leading the university as it celebrated its 150th anniversary last year, and its establishment as New Zealand's first university, Dr Somerville said.
Prof Hayne showed compassion for the university community during this year's Covid-19 pandemic, he said.
He wished her success in her new role and said an extensive global recruitment search for a new vice-chancellor would start soon.
Before becoming vice-chancellor, Prof Hayne was research and enterprise deputy vice-chancellor and head of the psychology department. She has been employed by the University of Otago since 1992.
There was plenty of work to get on with in the next six months, including overseeing the university's Vision 2040 strategy, she said.
Prof Hayne wished the university council well in finding a replacement vice-chancellor.
“This is a wonderful job. I am sure that they will find someone wonderful to lead the next chapter in Otago’s distinguished history.
“Saying goodbye to Otago will be very hard for me, but at the same time, I am looking forward to a new adventure at Curtin University.
"Once the borders open again for travel, I look forward to welcoming my Otago friends and colleagues to Australia.”