Former All Black Bill Osborne will become acting chairman.
Coutts said she was proud of what the company had achieved in her time on the board.
"While there have been many challenges in my time at Ports of Auckland, including the debate on port location and recent challenges as a result of Covid-19, overall the company has performed well in this time.
"Looking to the future, the 30-year master plan and automation project will be transformational. It will nearly double port capacity, improve safety and efficiency, and provide a range of benefits to Aucklanders,'' she said.
"Being chair of Ports of Auckland during five years of unprecedented challenges has been a privilege for which I will always be both grateful and proud.''
Staff at Ports of Auckland ''should be proud'' of their achievements and can feel confident that the company is set up for an exciting and successful future."
Osborne joined the board in May 2017.
He is a professional director, chairs Page & Macrae Ltd, and on the board of Transpower. He's president of New Zealand Rugby. Recent directorships include Planttech Research, CoreLogic NZ, and 2Degrees mobile. Osborne is a former group manager, international, for NZ Post.
Ports of Auckland, the country's main port for imports and owned by the Auckland Council, has been having a rough time in public perception of its efficiency, and value to Auckland ratepayers.
Closely after intensive public championing by political party NZ First, ejected from Parliament in November, to shut down the port's commercial operations on prime Auckland CBD land and move them to Northland's Northport, the port has become the most visible casualty of Covid-19 global shipping congestion, unloading delays and an upper North Island freight jam.
However not all in the supply chain accept that the pandemic is mostly to blame in Auckland port's case.
The announcement of Coutts' move comes as the port company, in its latest update to shipping and sector customers, advises the status of service level at its container terminal remained "severely degraded, major delays".
Labour supply continues to be described as "tight".
It's a status that customers have seen in updates for several weeks now as the port continues to struggle with shipping congestion and long delays unloading arriving ships - an issue it partly attributes to the impact of the pandemic on global container shipping, as demands for imported goods from travel-limited, locked-down consumers soars and air freight capacity shrinks.
Port management has also blamed the hangover from port labour strikes in Australia last year delaying ship schedules, but transport and logistics sector critics have increasingly pointed to the failure so far of the Ports of Auckland to fully implement a bold four year-long automation project - the cost of which is being kept secret by the port company and the council.
Sector insiders believe it has run into $400 million yet is still not working properly.
Along with being pilloried by the logistics sector for its poor productivity in recent years, the port company has disappointed Auckland ratepayers by advising it will deliver a much-reduced dividend to them until 2023 due to investment in the automation project.
Last year, Auckland Business Chamber chief executive Michael Barnett raised the question with the Herald of a more appropriate and value-returning ownership of the port - which has assets of more than $2 billion.
On December 10, Auckland mayor Phil Goff refused to express confidence in port chief executive Tony Gibson over safety issues and container ship delays at the port in Auckland's CBD.
