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.
Pato will join Sao Paulo on loan until Dec. 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 Corinthians spokesman.
Pato also retains the option to move elsewhere should any club bid 15 million euros for his services when the European transfer window reopens in the summer.
Anger among Corinthians supporters has risen after four straight defeats, with the club's players having hired personal security in light of the recent protests.