Other Australian cities had cancelled their celebrations due to the worsening wildfire risk in the oppressive summer heat.
Pressure had built for Sydney's spectacle to be scrapped before the New South Wales Rural Fire Service approved the event on Monday.
The popular celebrations are expected to attract one million people to Sydney Harbour's famous foreshore and generate 130 million Australian dollars (£69 million) for the state's economy.
An estimated one billion people worldwide watched last year's display on television.
Australia's most populous state has borne the brunt of wildfires that have killed nine people and razed more than 1,000 homes across the country in the past few months.
Of the 97 fires burning across New South Wales on Monday, 43 were not yet contained. A total fire ban was in place in Sydney, Canberra and other places to prevent new fires.
Temperatures on Tuesday were set to hit 33C in Sydney, with hotter weather in the western suburbs.
Thick smoke that has shrouded the city's iconic landmarks is also expected.
"Hot air is coming out of the centre of Australia, it's particularly dry and then unfortunately conditions are expected to worsen in New South Wales as we head into Tuesday," Rural Fire Services Commissioner Shane Fitzsimmons said.
Australian prime minister Scott Morrison said earlier that the fireworks should go ahead to show the world Australia's resiliency.
New South Wales deputy premier John Barilaro had said the spectacle should be called off.
"The risk is too high and we must respect our exhausted volunteers," he wrote on social media before the exemption was granted.
The western suburb of Parramatta decided to forego a fireworks display.
"Council was not granted an exemption to proceed with its fireworks display, due to the total fire ban in place and a range of associated risks," Mayor Bob Dwyer said.
In Australia's second-most populous state of Victoria, out-of-control wildfires are forcing thousands of residents and holidaymakers to evacuate. Melbourne, Victoria's capital, peaked at 41C on Monday with areas south-west of the city reaching 44C.
Lightning started 16 fires in Victoria overnight.
Cooler temperatures were expected to sweep into the state later on Monday, but windy conditions and thunderstorms heightened the risk of wildfires spreading.
Victoria emergency management commissioner Andrew Crisp said fires had generated their own thunderstorms, creating "unpredictable and dangerous" conditions.
He said there had been no confirmed loss of properties in the region.
Victoria emergency services minister Lisa Neville said the worst could be ahead. "This is not yet over. We're really only halfway through what is ahead of us here," she said.
In the national capital, Canberra, fireworks were cancelled and event organisers said other activities, including live music performances, could also be cancelled.
"It is a sensible decision for us not to proceed with the fireworks," the capital territory's emergency services agency commissioner Georgeina Whelan said.