The Brazil international has returned to South America after leaving for San Siro in 2007, and will wear the No. 7 shirt at the reigning Club World Cup champions
The Brazil international has penned a four-year deal with Timao, and he will wear the No. 7 shirt at his new side.
The €15m paid to the Rossoneri buys all of the attacker in economical terms, but Pato has negotiated 40 per cent of his rights for future sale in exchange for not being given a signing-on fee.
"I wish to say to goodbye, but above all to thank many people. From the president [Silvio Berlusconi] to the many people of Milan with whom I worked in these unforgettable years at the club," he said.
"I am going to Corinthians in Brazil for the chance to play more frequently. I will not, however, easily forget Milan. I am and always will be tied to the shirt, its colours and all the Rossoneri fans.
"Above all this message goes out to them, at this time, both my thoughts and my greatest thanks."
The former Internacional forward made 150 appearances for Milan since his arrival at San Siro in 2007, and he scored 63 goals in the process.
The 23-year-old was one of two Brazilians looking for a route out of the Serie A side in the January transfer window, though Robinho is yet to find a club willing to take him under their wing.
Pato has suffered an injury-strewn career at the Italian club and the Corinthians' move could allow him a fresh start, with World Cup 2014 less than 18 months from kicking off in Brazil.