In a rematch of this year's third-place play-off, which Argentina won as Lionel Messi and Gary Medel were sent off, the teams will meet again at the El Monumental on June 12 next year.
While the draw took place on Tuesday, the nations already knew almost all of their opponents with teams split into zones for next year's tournament in Argentina and Colombia.
However, Australia – playing at their first Copa America – were drawn into Group A, which features Argentina, Bolivia, Uruguay, Chile and Paraguay.
Qatar, the other invited nation, will meet Colombia, Brazil, Venezuela, Ecuador and Peru.
Brazil will go into the tournament as defending champions after their success at home this year.
The top four teams in each group will advance to the quarter-finals.
Group A: Argentina, Australia, Bolivia, Uruguay, Chile, Paraguay.
Group B: Colombia, Brazil, Qatar, Venezuela, Ecuador, Peru.