The Gunners have not commented on Santos' future but reports of a return to his homeland on loan surfaced after he was photographed arriving in Porto Alegre on Sunday.
The 29-year-old has now revealed his reasons for making the move to Gremio, saying that he is looking forward to the challenge and excited about playing under Vanderlei Luxemburgo.
"I have the best expectations," he told Lancenet at the airport. "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 Luxemburgo. He is a top manager in our football."
Santos is keen to play regularly after struggling to establish himself at Arsenal, but accepts that it will take time for him to get into peak condition.
"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 explained.
"I'll need five or six games to be fitter. I'm anxious to know the squad."