The competition was set to go ahead on November 16 during the six-week break in domestic football, but the Scottish champions have now pulled out after a backlash from fans.
The mini-tournament was set to feature the first Old Firm derby match outside of Scotland, with Australian sides Western Sydney Wanderers and Sydney FC also featuring.
Rangers' withdrawal came after concerns were raised with organisers, which resulted in the their agreement being terminated.
Reports from Sky Sports claim the Glasgow giants were not happy with the the timing of the announcements for the tournament and the failure to use 'Old Firm' in branding.
A statement on the club's official website said: "After it became clear the tournament organisers were unwilling to fulfil their commitments to Rangers, we have, with immediate effect, terminated the club's agreement with the organisers."
Former Celtic boss Neil Lennon joined talkSPORT's Jim White to react to the news, and said it was the wrong call to scrap the Old Firm Down Under, insisting it was a great chance to sell both clubs and Scottish football as a whole overseas.
He also accused Rangers of being 'small-minded' in their decision making over the snub.
"I think certainly financially, and commercially, it is a missed opportunity", Lennon told talkSPORT.
"Given what it would have meant to both clubs, in terms of revenue, and obviously selling the profile of both clubs worldwide, they [Rangers] have reasons behind it.
"I know there was a lot of decent chat around it from both sets of supporters with the game going ahead, but it is a shame because there is not a lot of money coming into the Scottish game, compared to the other leagues around the world.
"This was an opportunity to sell the game, and unfortunately for many reasons, a lot of them might be 'small minded', and it is not going to happen. I think it is a shame", Lennon added.
The decision to take Scotland's famous rivalry aboard was met by an almighty backlash from both sets of fans - in a rare moment of unity between the Celtic and Rangers supporters.
Fans unfurled banners at their home games following the initial news, with the Hoops faithful's reading 'Shove your 'Old Firm' friendly up your a***', and the Gers' saying 'Money over morals, no derby friendlies'.
While both sides of the Glasgow divide will likely be happy with Rangers' exit, the co-promoters of the Sydney Super Cup were less impressed.
In a joint statement, TEG Sport and Left Field Live said: "We were disappointed to wake up this morning to Rangers FC's statement that it will not be participating in the Sydney Super Cup.
"The Rangers Board committed to these matches following extensive negotiations over eight months. Seemingly in response to negative fan reaction, they have pulled out of their contracted commitment.
"We have worked closely with all stakeholders to bring this exciting event to Sydney, and we refute any suggestion that we were unwilling to fulfill our commitments to Rangers. We have acted in good faith and have put the event on sale with a great response from fans here.
"In changing their minds, the Rangers Board has let down many many fans in Australia and the Asian region. We will now consult with our stakeholders before determining our response."
Rangers take on Celtic this Sunday in the Scottish Premiership as the Old Firm rivalry continues.
The Bhoys are currently three points ahead of their arch-rivals and current league champions, but Giovanni van Bronckhorst's side can go level on points with Ange Postecoglou's men should they secure victory.