The five-time world champions meet the Socceroos at the Melbourne Cricket Ground, Victoria, four days after a clash with old rivals Argentina at the same venue.
The official announcement was made by the Victorian Government on Thursday, at 09:00am local time.
The Australian double-header be the first official friendly fixtures under new coach Tite, who has led his side to six consecutive victories in World Cup qualifying since his June 2016 appointment.
Brazil last met Australia in September 2013, when two goals from Jo, and strikes for Neymar, Ramires Pato and Luiz Gustavo saw the Selecao run out 6-0 winners at the Mane Garrincha stadium in Brasilia.
Brazil and Australia have met seven times previously, with the Selecao triumphing on five occasions, and the Socceroos' only victory arriving in the 2001 Confederations Cup.
June’s matches will see Brazil return to Melbourne for the first time since 1988 when they participated in the Australia Bicentenary Gold Cup.
Chevrolet Brasil Global Tour
Australia v Brazil
Melbourne Cricket Ground, Victoria
Tuesday 13 June 2017
20:05 (AEST) Local Time
07:05 (BRT) Brazilian Time
07:05 (ART) Argentinian Time
11:05 (BST) London Time