Robinson had hoped that extensive rehab would allow him to secure a place in his country's 30-man squad but the 27-year-old admitted he will be now be forced to watch the tournament from the sidelines.
"Pushed really hard to make it, but knee just isn't right!! Very disheartening!!" Robinson tweeted.
"You never want to go into a game with the thought in the back of your mind that you might not be right. So I made the decision. My knee is just not right. It's been on my mind for a while but (yesterday) it just came to a head," Robinson told The Australian newspaper.
"There were a few little hiccups along the way and I realised last week I was coming to the end of a dead end.
"There was always the risk was that if I kept going and tried to play without an ACL I was going to do myself even more damage."
The Waratahs forward said he was "heading in for surgery tomorrow", two days before Robbie Deans is due to name his final squad.
The news is a major disappointment for Deans and fellow Wallabies selectors Jim Williams and David Nuciferia as a fit and in-form Robinson would have been a definite starter for their World Cup opener against Italy on September 11.
Robinson has established himself as one of the world's leading tightheads in recent seasons, helping to stabilise an Australian scrum that, while battered by England last summer, has grown in stature since the last World Cup.
But while the news is a big blow for the Wallabies, it hasn't come as a major surprise. Media reports had initially ruled Robinson out of the World Cup when he suffered the injury in national training in early July, with his attempts to delay surgery in favour of the rehab route leaving Australian fans hopeful rather than expectant.
Deans will now hope that the seven remaining injured players in contention for a squad spot will prove their fitness at a specially-arranged testing session this Wednesday.
Doubts still surround the availability of hooker Tatafu Polota-Nau, props James Slipper and Ben Dale, No8 Wycliff Palu, wing Drew Mitchell and centres Berrick Barnes and Rob Horne.