Santos moved to Arsenal from Fenerbahce in August 2011, but has failed to hold down a regular place in Arsene Wenger's first team.
The form of Kieran Gibbs and the arrival of Nacho Monreal means the Brazilian left-back has made only six starts for the Londoners this season and he has now been given a chance to play regular football back in his homeland.
Many had expected Wenger to hang on to Santos until the end of the season once Gibbs was ruled out for two months with a thigh injury, but the Arsenal boss has decided to let the £6.8million man depart for the Porto Alegre-based club.
Wenger will not be able to use Monreal in the Champions League as he is cup-tied, but the Frenchman is happy enough to deploy Thomas Vermaelen in that position in the competition.
Santos, who has had spells with Brazilian clubs Corinthians, Atletico Mineiro, Flamengo and Figueirense, has turned out 36 times for the Gunners during his time in north London.
He infuriated Wenger and the Arsenal support when he asked former team-mate Robin van Persie to swap shirts at half-time during the 2-1 defeat at Manchester United last November.
Source: PA
Source: PA