People queued for pubs and bars that opened at midnight on Monday specifically for the occasion.
Many others have been enjoying anticipated reunions and visits to the homes of relatives and friends.
Covid rules had banned household visits and travel beyond a 5km (3.1 miles) zone, separating many families.
But most restrictions have now been eased for fully vaccinated people.
People can now share meal together at reopened cafes and restaurants, and visit gyms and other shops. There were long queues for barbers, nail salons and beauticians on Monday.
Australia's biggest city was allowed to exit lockdown after the state of New South Wales (NSW) reached a 70% double-dose vaccination target for over-16s.
More restrictions will ease when 80% of over-16s are fully vaccinated. Currently, over 90% have received a first dose.
"It's been a difficult 100 days," state Premier Dominic Perrottet said on Monday.
"But the efforts that people have made right across the state, to go out and get vaccinated, has enabled this great day."
Mr Perrottet warned that NSW was bracing for a surge in Covid cases, but said the healthcare system had been preparing for weeks.
"We'll see hospitalisations increase… but we need to learn to live alongside the virus," he said.
The state has not yet imposed a system to check vaccination status, leaving it up to individual businesses.
Sydney's lockdown began in late June after a Delta variant outbreak took hold, leading to tens of thousands of infections.
It spread to Melbourne and Canberra, prompting those capitals to go into lockdown, as well as to New Zealand.
Canberra is due to exit lockdown on Friday, while Melbourne is predicted to reopen in late October.
Australia had previously adhered to a Covid elimination strategy, and this remains the objective in some states.
But the rapid spread of the Delta variant forced a greater focus on vaccination efforts so Australia could switch to "living with the virus".
Queensland, Western Australia, South Australia, Tasmania and the Northern Territory remain largely virus-free.
Authorities have flagged that Australians living abroad could travel back into Sydney next month, as the nation's borders reopen.