Pato enjoyed a fruitless spell with Milan and was keen to make the return to his homeland after a difficult time.
In a statement published on AC Milan’s official website, he said: “I am going to Brazil to play consistently, but it won’t be easy to forget.
“I wish to salute, but above all to thank, everyone from the President to the many people I worked with in these unforgettable years at Milan.
“I am going to Brazil, to Corinthians, so I’ll have the opportunity to play consistently. It won’t, however, be easy to forget Milan.
“I am and always will be very tied to this jersey, the club colours and all the Rossoneri fans. Above all at this moment my thoughts and my biggest thanks go to them.”