However, he will not be allowed to play in the return match on June 15, which is one day before the world champions face Greece in their opening Confederations game in Germany.
"I had a conversation with (coach Carlos Alberto) Parreira and it was agreed I will play (in the Cup final) on June 12 and report for Brazil the next day," Adriano told reporters on Tuesday.
Parreira said: "It would be ideal to have the player for the whole preparation period. But it's an important game for his club and he will only miss one day of training in Germany."
Adriano has also been included in Brazil's squad for the World Cup qualifiers at home to Paraguay on Sunday and in Argentina three days later.
Despite his excellent form for Inter this season, Adriano has been a substitute for Brazil.
But Ronaldo's exclusion from the Confederations squad appears to have opened up a place for him.
Ronaldo was omitted at his own request after saying that he needed a rest.
The Real Madrid player has also been left out for the two World Cup qualifiers.
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