The forward has departed on loan because of fears for his safety, after fans attacked players in a training-ground incident last weekend
The Brazil international only arrived at Pacaembu from AC Milan in January of last year but was reportedly left with fears for his safety after Timao supporters invaded the club's training ground at the weekend, forcing the 24-year-old forward and a number of his colleagues to barricade themselves in the dressing rooms.
Pato will join Sao Paulo on loan until December 2015, with Corinthians set to continue paying half of his wages, but the Jadson deal is a permanent transfer.
"The clubs, Corinthians and Sao Paulo, have signed the contract and it just remains for the players to sign," said a Timao spokesman.
Pato also retains the option to move elsewhere should any club bid €15 million (£12.5m) for his services when the European transfer window reopens, or even return to Corinthians at the end of next year.
Anger among Corinthians supporters has risen after four straight defeats, with a number of the club's players having hired personal security in light of the weekend attacks.