The Frenchman was heavily linked with a switch to the Copa Libertadores champions in recent days and Kalil took to Twitter to confirm the news.
He wrote: "Anelka is a rooster," in reference to the club's mascot.
The 35-year-old will join up with the likes of Ronaldinho with the Brazilian outfit after enduring a tumultuous few months in Europe.
The Football Association wrote to FIFA last month requesting that Anelka's ban be applied worldwide.
On Saturday, the former Arsenal and Chelsea striker confirmed that he had received offers from a number of clubs but played down the prospect of accepting any move in the near future.