The Brazil international failed to establish himself at the Emirates after manager Arsene Wenger paid Fenerbahce 7m euros for his services in August 2011 and has now returned to his homeland.
A statement on the Gunners' website read: "After finding first-team opportunities limited this term, Santos now returns to Brazil's Serie A - the Brasileirao - for more regular first-team football. Everyone wishes Andre well for his time with the Tricolo."
Santos, 29, had previously commented on his way out of England: "I have the best expectations. They are one of the biggest clubs in the country. I've come to Gremio to be a champion. I am very excited about this project.
"I have dreamed of working with (Gremio manager) Vanderlai Luxemburgo. He is a top manager in our football."
One of the main criticisms levelled at Santos was a perceived lack of match fitness - but he remains adamant that regular playing time will quickly solve the problem.
"If there was a game today, I would like to play. But I need to be match fit as I played a game one day, then not the next one," he added.
"I'll need five or six games to be fitter. I'm anxious to know the squad."
Santos also hopes the move boosts his chances of forcing a way back into Brazil's team, as he added: "All players want to return to the national team and I'm no different."
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