Scrivener's departure will bring to an end a two-year association with the capital club, where he initially acted as an assistant coach specialising in defence.
Explaining his decision, Scrivener said: "This has been a massively difficult call to make, because I've thoroughly enjoyed my time at Edinburgh and feel I've progressed as a coach through working with different people and in different competitions.
"I've met some great individuals both among the squad and the management team, and I've got faith in their ability to take the club forward.
"I'm a rugby man, but first and foremost I'm a family man. My wife and daughters have made huge sacrifices to support me in the last couple of years, and having had the chance to further discuss our future with them, I've chosen to withdraw my application and head back to Australia."
"My focus now is on helping Edinburgh follow up Saturday's great result against the Ospreys by winning our last four Magners League games."
Craig Docherty, the club's chief executive, said: "We respect Nick's decision and his desire to be closer to his young family. The process of identifying and appointing a permanent head coach is ongoing, and we're working extremely hard to bring in an individual who will ensure the club keeps progressing."
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