Asian Cup holder Qatar has been drawn in Group B and will face co-hosts Colombia, defending champions Brazil, Ecuador, Peru and Venezuela.
Argentina will play host for one of the semi finals as the Monumental will be one of the two venues for one of the semi finals.
Australia's only win against Argentina in a men's worldwide came in 1988 when it famously triumphed 4-1 in Sydney, with Arnold featuring in the home side's line-up.
The mascot of the Copa America 2020, Pibe, presents the official ball of the football tournament during the championship's draw at the Convention Centre in Cartagena, Colombia.
The 2020 tournament will also see a change in format.
Australia and Qatar are now involved in AFC Round 2 qualifying for the 2022 FIFA World Cup™, with Qatar taking part due to the tournament doubling as 2023 AFC Asian Cup qualifying.
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General view of the completed draw on the big screen. Argentina defeated Chile in the third place play-off at this year's tournament.
No guest nation has won the Copa America, with Mexico coming closest by reaching the final in 1993 and 2001. Eight teams, or the top four from each group, make it through to the quarterfinals.
Co-host Argentina will open the tournament on 12 June with a match-up against Chile in Buenos Aires as the pair reprise their recent rivalry.
Japan, the other invited nation, also failed to win any of its games as it was held to draws against Uruguay and Ecuador following a heavy 4-0 defeat against Chile in their opening match.
"The Copa America is the oldest global football competition in the world and we are honoured to have received an invitation to compete", said Socceroos coach Graham Arnold.
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