Hegarty was handed the caretaker position until the end of the season in September following the departure of manager Peter Hutton.
Derry were in relegation trouble when the former Brandywell player arrived but Hegarty guided the team to safety.
However, his decision leaves City in search of a new manager for 2016.
Caretaker boss Paul Hegarty has declined Derry City's offer to take over as manager because of personal reasons.