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.
Airlines Qantas, Jetstar and Air New Zealand will all fly routes between the two countries.
Australia and New Zealand shut their borders in March last year and brought in compulsory quarantine for returning nationals.
Since October, New Zealand travellers have been allowed to enter most Australian states without quarantine, though this had not been reciprocated amid concerns about sporadic Covid outbreaks.