Alexandre Pato has been allowed to link up with Sao Paulo, with Jadson moving in the opposite direction to Corinthians.
Pato moves on a two-year loan deal, while Jadson has penned a permanent contract.
The deal involves two Brazil internationals and two men who have shone in Europe in the not too distant past - for AC Milan and Shakhtar Donetsk respectively.
A return to Europe for Pato has been mooted for some time, with leading lights in England, Spain and Italy said to be monitoring his situation.
He is, however, to remain in his homeland after being allowed to move on by Corinthians.
Manager Mano Menezes told UOL: "Regarding Pato and Jadson, it became a possibility and we came to the conclusion that, due to the circumstances, it would be good for us.
"Jadson will be another option as a playmaker, something we need.
"Pato probably understands. So do Sao Paulo. Everyone, given the circumstances, understood that it would be good to make this deal happen to improve everything for everyone.
"When opportunities like this one come up, as this did, we can't waste them."