CONMEBOL's deputy general secretary Gonzalo Belloso said that the two members of the Asian Football Confederation (AFC) would not be able to participate due to a clash with World Cup qualifying dates.
"The Copa America is absolutely going ahead. But Qatar and Australia, who had asked to take part, will not be able to come," Belloso told Argentine radio La Red.
"The Asian confederation has programmed World Cup qualification on the same dates as the Copa."
Although Qatar is hosting the 2022 World Cup, it is taking part in the preliminary campaign because it is doubling up as qualification for the 2023 Asian Cup in China.
The AFC has scheduled qualification matches for 11 and 15 June.
The Copa, which was postponed last year due to the coronavirus pandemic, begins on June 11 and will be played in Argentina and Colombia.
The loss of the two invitational teams to South America's showcase tournament for national squads will not affect the Copa America programme, Belloso said.
"The days of the invitees' games, the teams" that would have played them "will be free. The Copa will have all its splendour," he said.
It will be the first time the Copa is played in two countries. The Monumental stadium in Buenos Aires will host the opening match between Argentina and Chile.
The final will be played at the Metro stadium in Barranquilla, Colombia on July 10.
Qatar, which was also invited to the 2019 Copa America, were due to play in Group B alongside champions Brazil, Colombia, Venezuela, Ecuador and Peru.
Australia, which would have participated for the first time, was pitched with Argentina, Chile, Uruguay, Bolivia and Paraguay.