The duo will face off in a Grand Slam first round for the second time after 15-year-old Gauff famously beat Williams at Wimbledon last summer.
Elsewhere, Roger Federer and Novak Djokovic were drawn in the same half of the men's bracket, meaning they are on course for a possible semi-final showdown; they will face Steve Johnson and Jan-Lennard Struff, respectively, in the opening round.
Men's top seed Rafael Nadal faces Hugo Dellien in his opener, and Serena Williams takes on Anastasia Potapova.
Williams has been placed in a challenging quarter of the draw, which includes her sister Venus, Gauff and defending champion Naomi Osaka, per Christopher Clarey of the New York Times:
Ben Rothenberg of the New York Times provided the draw in full for both the men's and women's singles:
Jose Morgado of Record noted there are a number of huge names in action on the first day of the competition proper:
One of the biggest stories in tennis last season was the emergence of Gauff, who captured the imagination of fans with her performances at SW19.
She produced some brilliant displays to advance into the fourth round of the competition, although the victory over Venus was arguably the most memorable:
Elsewhere in the women's bracket, Serena will be out to win her first Grand Slam since her 2017 success in Melbourne. She has made it to four major finals since—two at Wimbledon and two at the U.S. Open—but has failed to get over the line in any.
The top seed in the women's draw will be Ashleigh Barty, who will be desperate to make history in front of her own fans. The French Open champion begins her quest for glory Down Under up against Lesia Tsurenko.
In the men's singles, the big names are expected to be difficult to beat again. While Nadal is the top seed, Djokovic is the favourite for many, especially after he dominated the Spaniard in the final in Melbourne a year ago.
Before Thursday's draw, Djokovic reflected on that display in 2019:
To get to that stage this year and compete for an eighth Australian Open title, Djokovic will need to be at his best. Struff is among the toughest players the Serb could have been pitted against in the first round, while Federer will potentially stand between him and the final.
If anyone is to end the dominance of Djokovic, Federer and Nadal in Grand Slams, it may be fourth seed Daniil Medvedev. After making it to the final of the U.S. Open last year, where he was beaten by Nadal, the Russian starts against Frances Tiafoe in the first major tournament of the year.