The company announced in a statement that Mr Costelloe had left the role on Monday, and would be departing Delta.
Over his tenure, he had been instrumental in guiding Delta through various challenges and had earned the respect and admiration of employees, stakeholders and customers, it said.
The board of directors had decided to implement this leadership change as part of "a strategic effort to better position Delta for future opportunities".
This transition would build upon the strong foundations established by Mr Costelloe and would focus on reinforcing financial stability.
Board chairman Peter Carnahan extended the company’s gratitude and heartfelt thanks to Mr Costelloe for his "significant contribution" to Delta.
"His leadership has been marked by integrity and commitment."
A member of Delta’s leadership team would take on the role of acting chief executive and a recruitment process was under way to find a suitable replacement, the statement said.
Mr Carnahan declined to comment when asked to clarify if Mr Costelloe had resigned.
