The 23-year-old has reportedly signed a four-year deal 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.
Corinthians later confirmed a €15million deal had been done, pending a medical.
The club have already handed Pato, whose face welcomed visitors to the club's website tonight, the number seven jersey.
"In the coming days Pato, who will wear the number seven shirt with O Timao, will undergo medical tests and sign a contract for four seasons," the statement read.
"Corinthians have bought 100 per cent of the economic rights of Alexandre Pato for €15million."
Pato quickly established himself as a favourite at Milan after signing from Internacional in 2007, scoring nine goals in his first half-season and reaching double figures in each of the next three campaigns.
However, he scored only once in Serie A and four times altogether last season and has made only seven appearances in all competitions so far this term as injuries have hampered his progress.
Following his medical Pato is due to join up with his new team-mates, who have not played since their 1-0 FIFA Club World Cup final triumph over Chelsea last month, for pre-season training ahead of their match away to Paulista on 20 January.