Australia is one of two guest nations competing in the tournament, along with Qatar.
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 co-hosts Argentina and Colombia, which are separated by some 4,350 miles (7,000 kilometers).
Scaloni's men beat Chile in the third-place play-off this year, in a game that saw Messi and Gary Medel sent off.
All dates are local times, and venues are not yet confirmed, with the Argentina clash possibly being held in River Plate's El Monumental stadium instead of Boca Juniors' La Bombonera as originally planned.
Argentina last won the Copa America in 1993 and the nation is desperate to finally get their hands on the trophy once again.
"Adding the Copa America to our schedule next year will mean that the Socceroos will play at least 14 matches throughout 2020".
The top four teams from each group at the 2020 Copa America qualify for the quarterfinals.
The June 12-July 12 tournament is the 47th edition of the Copa America, the oldest worldwide competition in world football.