The 34-year-old Serb said he practised on court in Melbourne within hours of leaving an immigration detention hotel.
But Australia's immigration minister still has powers to re-cancel the visa and deport the unvaccinated player.
"Despite all that has happened, I want to stay and try to compete in the Australian Open," Djokovic tweeted.
The statement continued: "I remain focused on that. I flew here to play at one of the most important events we have in front of the amazing fans."
Djokovic also posted a photo of himself and his team - including coach Goran Ivanisevic - on court at the Rod Laver Arena, where he has won a record nine men's singles titles.
The Australian Open begins on 17 January and if Djokovic wins, he will become the most successful men's player in history.
The world number one is tied with Switzerland's Roger Federer and Spain's Rafael Nadal on 20 Grand Slam singles titles.