The 23-year-old has reportedly signed a four-year deal with the recently-crowned Club World Cup champions after revealing his desire to return to his homeland last month.
Milan confirmed Pato's departure, after five years at San Siro, in a brief statement on their website.
"AC Milan can announce that Alexandre Pato has been sold outright to Sporting Club Corinthians Paulista," the statement read.
Pato told Milan's official website: "I wish to say goodbye, but especially thank you to everyone from the president to the big number of people with whom I worked in these unforgettable years in Milan.
"I go to Brazil, at Corinthians, to have the possibility to play with regularly. It won't be easy, anyway, forgetting Milan.
"I am and I always will be bound to this jersey, to its colours and to the whole supporters. Especially in this moment, my thoughts and thanks go to them"