Earlier this month, the Brazilian Football Confederation (CBF) announced they would fight the European champions' insistence that the forward would only be available for one tournament.
Now, however, Barca claim that CBF president Marco Polo del Nero has agreed that Neymar will be called up solely for the Olympics in Rio de Janeiro.
A club statement reads: "FC Barcelona thanks the Brazilian Football Confederation and its president, Marco Polo del Nero, for having accepted the proposal the club made so that Neymar would only play the Olympic Games that take place between August 3 and 21.
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"As a result, Neymar Jr will be exempted from playing the Copa America that takes place in United States between June 3 and 26."
The Copa America is taking place for a second consecutive year to mark the centenary of Conmebol and the first tournament in 1916.
It will be hosted outside of South America, in the United States, for the first time and features an expanded field of 16 teams including six Concacaf representatives.
Neymar was sent off at the end of Brazil's second match of last summer's Copa America in Chile, resulting in a four-match ban which ruled him out of the rest of the tournament.