The north Wales health board was first put under the measures in June 2015 following "long-standing concerns about governance, leadership and other issues".
Jo Whitehead, currently the Chief Executive of Mackay Hospital and Health Service in Queensland, Australia, will take up the role in January 2021.
The Robin Holden report was completed in 2014, after staff blew the whistle with their concerns over patient safety and fears some were being given sub-standard care on the Hergest Unit of Ysbyty Gwynedd.