Marseille striker Brandao has agreed a loan switch which will take him back to his native Brazil with Cruzeiro.
The agreement will run until the end of the year, but includes the option for a permanent deal to be struck in the summer.
The 30-year-old had made it clear over recent weeks that he needed to leave Stade Velodrome following difficulties in his private life.
Brandao is currently being investigated by French police over a rape allegation.
Marseille president Jean-Claude Dassier told the club's official website: "His departure was inevitable for us all. It was no longer possible for the player to go outside and playing at the Stade Velodrome in these circumstances became impossible.
"It's a blow for the club. One more blow. This season is decidedly complicated.
"But in our squad I know I can count on all the players and staff to make every effort to retain our title."
Dassier is disappointed to have seen Brandao leave, as he has been a key figure for Marseille since arriving from Shakhtar Donetsk in 2009.
"I wish Brandao every success in Brazil. He has joined a great club and I hope this will have a positive outcome," he said.
"I could not let him go without mentioning his future and everything he has done for the club.
"I reminded him it was thanks to his brace against Toulouse in the semi-finals last season we won our first trophy of 2010, the Coupe de La Ligue."