0753 GMT January 27, 2020
The Socceroos, one of two guest teams invited to the South American football championship, will also face Paraguay, Bolivia, Uruguay and Chile in Group A, AFP reported.
In Group B, Asian champion Qatar, the other guest nation, will face Colombia, Brazil, Venezuela, Ecuador and Peru, with all games taking place in Colombia.
The first round designations for Australia and Qatar were the only major issue left to be decided at Tuesday's ceremonial draw.
The other teams in the two groups had already been determined based on geographical proximity to cohosts Argentina and Colombia, which are separated by some 4,350 miles (7,000 kilometers).
Australia coach Graham Arnold said his team was relishing the prospect of facing Argentina in Buenos Aires.
"That's what it's all about, it's about testing ourselves at the highest level," Arnold said following the draw.
"The players are so excited to have this great opportunity."
The former international striker speaks from experience: Arnold was a member of the Socceroos team which lost to a Diego Maradona-inspired Argentina in a 1993 playoff for a spot in the 1994 World Cup.
"In the old days in the 1990s we played Argentina and Maradona over there and if you speak to the players involved they'll tell you what a great experience it was," Arnold said.
"Our boys haven't really had the experience of playing in South America. So to be able to play in South America in those great stadiums in that environment is going to be a buzz."
The 2020 Copa America marks the first time in the modern history of the tournament that the event is being cohosted.
Argentina and Colombia were chosen as hosts after South American football's governing body CONMEBOL turned down an offer from the US Soccer Federation to hold an expanded 16-team edition of the Copa America.
The 2020 tournament will also see a change in format.
At this year's Copa America, won by host nation Brazil, the 12 teams taking part in the event competed in three first round groups of four teams, with the top two in each group and the two best third placed teams advancing to the quarterfinals.
Next year, the tournament will instead see two first-round groups of six teams. The top four finishers in each group will qualify for the quarterfinals.
Tournament cohosts Argentina will kick off the tournament against bitter rival Chile on June 12 in Buenos Aires.
Chile scored back-to-back victories over Argentina in the finals of the Copa America in 2015 and 2016. Argentina defeated Chile in the third place playoff at this year's tournament.
The June 12-July 12 tournament is the 47th edition of the Copa America, the oldest international competition in world football.