With both North London clubs seemingly in need of a striker, former AC Milan forward Pato was strongly linked with a move in the January window.
However, it now looks likely that the fleet-footed forward will remain in his native Brazil for the foreseeable future.
Pato - who was signed for around 15 million euros from Serie A - was heavily criticised by the Corinthians fans who invaded the club's training ground to protest.
Fearing for his safety, Pato made it clear he no longer wanted to play for the club.
The Brazilian international is still only 24, and the decision to swap him for a 30-year-old midfielder have left some baffled.
However, Corinthians coach Mano Menezes maintains the move is a positive one.
"If we have decided to do this, you understand that we consider it to be a positive thing," he is quoted as saying on ESPN.
"The arrival of Jadson gives us the chance to do what we want to do, and it is positive for Pato as well.
"Sao Paulo thought the same as us. Everyone involved, under the circumstances, understood that this was a positive move to improve things for everyone."
The move will surely see both Arsenal and Tottenham pursue other targets this summer, while Pato will hope the move will aid his fight for a place in the Brazil squad this summer.