That will include AstraZeneca, Pfizer, Moderna, and Johnson & Johnson, along with China's Sinovac and the India-produced Covishield.
Unvaccinated people or those without approved jabs will require two weeks' managed isolation in hotels or dedicated facilities.
Lapreet Singh, a temporary visa holder, has been trying to return to Australia for 18 months after travelling to India to see his sick father.
He only spent a month in Australia, studying a business degree in Sydney before travelling overseas.
Mr Singh said it’s a long time coming.
“We have been waiting for nearly 18 months, and most of us on temporary visas have already got vaccinated,” he told SBS News.
“We are hoping to turn to Australia soon. Our lives have totally stopped.”
Prime Minister Scott Morrison said the recognition of the vaccines is an important next step in the national plan to reopen the country.
"They will be particularly important for those coming from countries where those vaccines are being used," he said.
"India is an obvious one of those, as is China and other countries throughout South East Asia."
"That will be important, also, when we move to the phase, which I believe will be occurring next year in some states, particularly in my discussions with New South Wales, where those students, skilled migrants, and perhaps sooner, will be able to come into the country and have those vaccines recognised as we move forward."
The peak body for universities said the TGA decision cleared the way for fully vaccinated students from China and India to re-join their friends on Australian university campuses in the near future.
“The decisions will bring fresh hope for more than 130,000 students who have been patiently waiting to return to Australia to complete their studies,” Universities Australia Chief Executive Catriona Jackson said.
“Nearly half of all international students in higher education remain outside of Australia. Around one-third of our international PhD students are also offshore, anxious to return to complete their research here.”
Tourism chiefs are also celebrating the decision.
“It's absolutely huge and something we've been banging on about for a number of months,” Margy Osmond, the chief executive of the Tourism and Transport Forum told ABC News.
“If we don't accept Sinovac, nobody from China will be coming here.”