Reports said it will be a "true rectangular" stadium, which would better suit popular local sports including rugby league and football.
The three main tenants of Allianz Stadium, the Waratahs, the NRL's Roosters and Sydney FC will be displaced from late 2018.
It is understood some also raised concerns about the $2.3 billion price tag, up from former premier Mike Baird's original estimate of $1.6 billion.
SCG Trust chairman Tony Shepherd argued his organisation had run out of money after spending $300 million trying to keep the "old and inadequate" Allianz stadium functioning.
The decision is expected to be announced tomorrow and brings to an end a saga that dragged out for more than 18 months since Mr Baird first detailed his proposal.
Click through to see all of the stadium's most momentous occasions.
The stadiums won't be available in 2020 but NRL chief executive Todd Greenberg assures fans that State of Origin and the grand final will remain in Sydney that year.
The overhaul, which will involve the ANZ Stadium at Sydney Olympic Park being substantially demolished and rebuilt from 2019, was reportedly signed off by cabinet on Thursday.
Sports Minister Stuart Ayres backed that option and has spent nearly two years tying himself into knots advocating various positions that would get it over the line.
Meanwhile, Opposition Leader Luke Foley has slammed the Moore Park redevelopment as a "white elephant", questioning the facility's ability to draw a capacity crowd.
"I'm not someone who doesn't deliberate on these decisions and we have done that in a very collegiate way", she said.
The stadium has been a regular venue for the annual National Rugby League grand finals, and hosted the 2003 Rugby World Cup finals, Bledisloe Cup matches and the 2015 AFC Asian Cup Final.
Why are we doing this? Is the (Super Rugby teams) Waratahs vs the Bulls in Super Rugby going to get 45,000 people? They struggle to get 10,000.