The 30-year-old signed joined the Gunners from Fenerbahce in August 2011 for a fee in the region of 7million euros (£5.9million).
However, he struggled to establish himself in the first team at the Emirates, making just 13 starts in 18 months at the club.
The Sao Paulo-born full-back secured a return to his homeland when he signed a short-term deal with Gremio back in February.
That deal is set to expire in July and the Brazilian club have confirmed they do not intend to turn the move permanent.
"We signed Andre Santos for Copa Libertadores and his contract expires in July," Gremio's director of football Marcos Chitolina told UOL.
"It would be too expensive for Gremio to renew his contract; he is a very expensive player.
"We thank him for everything he has done, but we will keep Alex Telles and Fabio Aurelio."