The Aboriginal flag will fly permanently atop the Sydney Harbour Bridge from Monday, following the NSW Government's decision to scrap a $25 million plan to install a third flag pole on the landmark.

After a week on the bridge as part of NAIDOC Week celebrations, the Aboriginal flag was due to be swapped out on Monday.

Premier Dominic Perrottet revealed on Sunday the Aboriginal flag will instead replace the NSW state flag year round with the $25m to be reallocated towards Closing the Gap initiatives.

Mr Perrottet labelled the move "a practical and pragmatic solution which makes sense" following a raft of backlash directed at the hefty price tag announced last month.

The Premier had previously questioned the figure and timeline, and said he would be looking towards alternative measures.

"I accept that there are challenges with it, but it certainly shouldn't be costing the taxpayers $25 million," Mr Perrottet said in June.

"I will come back to you once I've interrogated this to a much greater degree in terms of costing."

The move follows the Victorian Government's commitment to fly the Aboriginal flag on Melbourne's West Gate bridge announced last week.

The flag had similarly been flown on a rotational calendar in line with key dates for Indigenous celebration and acknowledgement.

It has now replaced the Victorian state flag on a permanent basis following NAIDOC Week.

The NSW flag is set to be relocated to a site on Macquarie street in Sydney's CBD.