The world number 50, a quarter-finalist at Melbourne Park last year and in 2018, later tweeted: “My two tests were less than 8 weeks apart. I was sick in November, totally healthy now.
“There’s not a single documented case where I would be contagious at this point.”
A spokesperson for COVID-19 Quarantine Victoria said it was common among people who had previously tested positive to “shed viral fragments for some time which can trigger another positive result”.
Tennis Australia said in a statement the decision to allow Sandgren to fly had been made after a review by medical officials.
“In the case of Tennys Sandgren, who has self-disclosed that he previously tested positive in late November, his medical file had to be reviewed by Victorian health authorities,” it said.
“Upon completion of that review he was cleared to fly.”
Tennis Australia said any athlete who has recovered from COVID-19 must undergo a similar health review and earn “special clearance” from the authorities before travelling to Australia.
Some 1200 players and coaching staff are set to begin arriving from Thursday for the tournament,running from February 8-21, which was delayed by three weeks.
Victoria, once Australia’s COVID-19 hotspot, has said it will impose the strongest protocols seen at any tennis tournament for those flying in.
Players and staff must isolate for two weeks before they can take part in warm-up events at Melbourne Park.
Tennis Australia said players would undergo a more rigorous testing schedule ahead of the Australian Open than most returning travellers.