Members of the public aged 40 and over can now make an appointment at the St George Hospital COVID-19 Vaccination Hub.
The hub, one of 11 vaccination hubs announced by NSW Health at the start of the year, was officially opened on March 10.
Healthcare workers were among the first to access the hub. Residential aged care and disability care facilities were also slated to receive the vaccine "as a priority" within the first few months of the rollout.
It is now open to the general public.
A South Eastern Sydney Local Health District (SESLHD) spokeswoman said it had been offering both the AstraZeneca and Pfizer vaccines since April 26.
"The clinic became public facing to those aged 40-49 (Pfizer vaccination) on Monday, May 17," she said.
"The clinic became public facing to those aged 50+ (AstraZeneca vaccination) on Monday, May 24."
She said people should check their eligibility and find a local vaccine provider by using the federal government's COVID-9 vaccine eligibility checker. You can do so by clicking here.
NSW Health says it is working closely with the Australian Government to plan and implement a safe and effective COVID-19 vaccination program in NSW.
"NSW Health COVID-19 vaccination clinics are open," it said.
"NSW Health vaccination clinics and participating general practices across the state are open for COVID-19 vaccination bookings.
"f you are eligible in phase 1a, phase 1b or aged 40 years or older you can book an appointment now.
"If you are aged 40-49 years you are now eligible to book an appointment to receive the Pfizer COVID-19 vaccine. You no longer need to register your interest."
Other vaccination hubs are located at RPA, Westmead, Liverpool Hornsby, Nepean, Newcastle, Wollongong, Coffs Harbour, Dubbo and Wagga Wagga hospitals.
The hubs are located at specific sites with the required storage, vaccine handling and administration capacity.
NSW Health opened a mass vaccincation centre at Sydney Olympic Park, Homebush, on May 10.
South Eastern Sydney Local Health District (SESLHD) said residents and staff of residential aged care and disability care facilities would also be among the first to receive the COVID-19 vaccine.
It said those people "most vulnerable to the effects of COVID-19 or who have the highest risk of being exposed to, or spreading, the virus", will receive the vaccine "as a priority" within the first few months of the rollout.
SESLHD said this includes some healthcare workers, staff working in designated quarantine facilities, and residents and staff of residential aged and disability care facilities.
The aim was to ensure "our staff can safely continue to provide care to the community".
Media reports about St George Hospital at Kogarah being chosen as one of just 11 COVID-19 vaccination hubs in NSW led SESLHD to issue a statement via its Facebook page that vaccination bookings could not yet be made.
"This is exciting news and we are looking forward to participating in the vaccination program. However, we are not currently taking bookings from the public," it said.
"A COVID-19 vaccine is expected to be available to the general public once the vaccine becomes available through general practice.
"We will keep the community updated on when vaccinations may be available to the public."
According to the NSW Health COVID-19 Vaccination in NSW: Fact Sheet for NSW Healthcare Workers, it was expected there would be "limited doses of the vaccine available in Australia" in the first few months of the vaccination program.
"During phase 1a, the priority groups will be offered the vaccines at designated vaccination hubs in the first instance," it said.
"In NSW, those hubs will be located at specific sites with the required storage, vaccine handling and administration capacity.
"NSW Health is planning for vaccination hubs located at RPA, Westmead and Liverpool hospitals, followed by Hornsby, St George, Nepean, Newcastle, Wollongong, Coffs Harbour, Dubbo and Wagga Wagga hospitals.
"If vaccine supply increases during phase 1a, additional vaccination hubs, spokes and outreach clinics may be able to be supported."