Manager Roberto Mancini said: "Robinho is someone who needs to be playing regularly and we wish him well for the period of his loan."
The 26 year-old, who began his career at Santos, will leave for Brazil on Sunday.
Robinho joined City from Real Madrid in the summer of 2008 for a British record transfer fee of £32.5 million, the club's first big signing under the ownership of Sheikh Mansour bin Zayed.
The Brazil forward initially impressed at City and ended his first season as the club's top scorer with 15 goals.
But his form tailed off and he was often criticised for his performances away from Eastlands.
This season he has struggled to hold down a first-team place, first under Mark Hughes and latterly under new boss Mancini.
Robinho has made no secret in recent days of his desire to return to his old club as he seeks to consolidate his place in the Brazil side ahead of this summer's World Cup.
The player's last appearance came in the 4-2 FA Cup win over Scunthorpe at the weekend, an occasion he marked with a goal.