However, unvaccinated people will be left hanging for access to "freedoms" that were due to kick in on 1 December.
They will now have to wait at least until 15 December or until 95 per cent of eligible people in NSW are fully vaccinated - whichever comes first.
"We believe that by moving that date back to the 15th of December it will incentivise and we are hopeful that we can get that right up to 95 per cent," Mr Perrottet told reporters on Tuesday.
"That will not just be nation-leading, it will be world-leading as well.
"That is the key to opening up."
Some 93.6 per cent of people aged 16 years and older have had one dose of a vaccine and 87.8 per cent are fully jabbed.
The further relaxation of COVID-19 restrictions comes after the state began transitioning out of a near four-month lockdown three weeks ago as the spread of the virus steadily declines.
Freedoms fast-tracked for fully vaccinated in NSW
The expedited roadmap was announced as the state on Tuesday reported 173 new local cases of COVID-19 and four deaths.
The new cases were recorded in the 24-hours to 8pm on Monday from 58,988 tests and rose by 38 cases from the previous day.
There are 333 COVID-19 patients in NSW hospitals and 72 are in ICU.
'Joyful and celebratory' Christmas
Meanwhile, the tourism and hospitality sectors are expected to make up for losses endured during months of COVID-19 lockdown ahead of what looks like a "joyful and celebratory" Christmas period.
Tourism & Transport Forum CEO Margy Osmond says the industry has been losing close to $4 billion a month with virtually no international visitors for almost two years.
On Monday, NSW began welcoming fully vaccinated Australians home from overseas, without requiring them to undergo quarantine.
The first international travelers are welcomed back to Australia
Fully-vaccinated people are also free to travel anywhere in the state, setting the scene for a revival of hard-hit tourism and hospitality businesses in the regions.
Bookings for summer holidays in NSW are at a premium with many holiday towns on the east coast already fully booked.
"What makes this Christmas very different from last Christmas is the fact that there's joy in the air," Ms Osmond told the Nine Network on Tuesday.
"There's a different kind of spirit this Christmas. It's going to be a very celebratory one," she said.