Ms Holgate accused the prime minister of humiliating her and said there were no legal grounds for her standing aside.
However, she formally resigned on Monday.
"The current issue I am managing is a significant distraction and I do not believe it is good for either Australia Post or my own personal wellbeing," she said in a statement.
"Consequently, I have made the difficult decision to resign, hoping it will allow the organisation to fully focus on serving our customers."
Her resignation is effectively immediately.
Ms Holgate will not seek financial compensation and has promised to cooperate with a four-week investigation into Australia Post, being conducted by the federal finance and communications departments.
In a joint statement, Communications Minister Paul Fletcher and Finance Minister Simon Birmingham said the government would consider the investigation's findings in due course.
The pair thanked Ms Holgate for her service and acknowledged Australia Post's frontline workers' commitment during the pandemic.
Australia Post chairman Lucio Di Bartolomeo said the board and management would also cooperate with the review.
He acknowledged Ms Holgate's contribution since being appointed to run the government-owned enterprise in October 2017.
"While noting the current review, I would like to acknowledge and recognise the significant contributions she has made during her tenure," Mr Di Bartolomeo said in a statement.
"During the last three years, Australia Post has reported significant growth as it continued to innovate and transform its operations and structures to best deliver for Australian communities and customers."
He described 2020 as one of the toughest years in Australia Post's history and acknowledged the efforts of staff to meet the challenges posed by coronavirus.
Ms Holgate is standing by the purchase of luxury watches, saying the executives involved sealed a banking deal worth $220 million.
"However, I deeply regret that a decision made two years ago, which was supported by the chair, to recognise the outstanding work of four employees has caused so much debate and distraction," she said.
"I appreciate the optics of the gifts involved did not pass the 'pub test' for many."
Ms Holgate said she had no animosity towards the government and enjoyed working with Mr Morrison and senior ministers during her time at the organisation.
The postal workers unions says there are still serious, systemic issues with management at Australia Post and the rest of the leadership team should be held accountable.
Shadow attorney-general Mark Dreyfus said Australians are more concerned about post being lost and late than issues around Ms Holgate.