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."