The TGA provisional approval is for individuals 16 years of age and older.
These priority groups are expected to include quarantine and border personnel, frontline health workers, aged care and disability staff and residents.
The TGA said the vaccine met the high safety, efficacy and quality standards required for approval and they are happy to allow the public to be inoculated.
"We will communicate openly and in a timely way about the vaccine rollout, so Canberrans will know when they can get the vaccine, how to get it and what to do when the time comes", the spokesperson said.
'Australians should take confidence in the thorough and careful approach taken by our world-class safety regulator, ' he said.
"Our priority has always been to keep Australians safe and protect lives and livelihoods", Mr Morrison said.
Federal Health Minister Greg Hunt said today's formal approval from the TGA was another "very important step forward" and the one-year anniversary of Australia's first case was a day worthy of a "brief reflection of the journey".
The vaccine approval helped to lift Australian shares at the start of the week, despite United States shares coming off the boil on Friday.
Gabe Newell: There are aspects of Cyberpunk 2077 that are just brilliant
Various bug fixes (related to, among other things, loading of saved games, opening / closing of game, point of no return). Many quest bugs have also been addressed, and the issue causing save files to baloon has been addressed as well.
Advice over vaccine safety for pregnant women is expected to be handed to the government before the jab starts to be administered.
"This approval by the TGA is one of the earliest in the world for a full approval", Mr Hunt said.
The two-dose regimen could not be imported into Australia until it was approved by the TGA and today's announcement means millions of doses of the drug can now be shipped from overseas.
However, the Health Department Secretary Brendan Murphy stated that Australia will face "major logistical issues" in its intentions to vaccine the Australian population, as have other countries around the world, as the vaccine is required to be transported and stored at minus 70 degrees.
He said the vaccine rollout would then be scaled up as the local production increased.
The Australian government has secured at least 10 million doses of the Pfizer vaccine and 140 million doses of COVID vaccines in total. In other countries such as the United Kingdom and U.S., the vaccines have been approved on an "interim" basis, without the full analysis and review that more commonly takes place.
Trials have proven the Pfizer/BioNTech vaccine to be 95% effective in preventing symptomatic cases of COVID-19.
As per the latest updates by Johns Hopkins University, Australia has reported 28,777 COVID-19 cases so far.
In stark contrast, there have been 25 million cases in the U.S. alone and in excess of 400,000 deaths.