"Over half a million Australians have already been able to download the international vaccine certificate," Mr Morrison told the Seven Network.
"We are very close now to the reciprocal arrangements with Singapore."
Source: Getty Images/ d3sign
Health Minister Greg Hunt said the changes were made in line with rising vaccination rates across the country.
"We want Australians to be able to reunite with their loved ones, whether it's for births, weddings or just to visit family," Mr Hunt said.
Australians will need to prove their are fully vaccinated an approved or recognised vaccine.
The second dose will need to have happened at least one week before travel.
While vaccines are only approved for people aged 12 and over, the travel changes will also apply to children under 12.
Those who aren't vaccinated will still need an exemption to travel overseas and will be subject to travel caps.
Australian citizens, permanent residents and their family will be let into the country first.
Home Affairs Minister Karen Andrews said the government was looking to welcome skilled workers and international students back by the end of the year.
"I look forward to further easing restrictions over coming weeks and months as more and more Australians become fully vaccinated," she said.
"The Morrison government stands ready to once more welcome a significant number of fully vaccinated people across Australia's international border."
It comes as the prime minister said the first-dose rate in Australia had surpassed the rate in the United States.
"The national plan is working. The national plan is about opening Australia up and that is because the vaccination rates are climbing so high," Mr Morrison said.