The long-awaited initiative removes the need for visitors to quarantine.
Both countries have contained Covid outbreaks and kept infection rates low, in large part due to hard borders.
Excited passengers crowded Australian airports ahead of reunions with family and friends.
Thousands of people are expected to travel on Monday with some rising before dawn to get ready to board.
"I didn't realise how emotional I was going to be today," passenger Dawn Tratt told the BBC at Sydney airport.