The Portuguese winger, who had been with Atletico since his £17 million move from Benfica in 2007, paid tribute to fans in emotional terms following the move.
"It is difficult for me; I can hardly speak because since I came to Atletico I have grown and become a better professional," he said.
"When I arrived I said I would do my best to win a title and I eventually ended up with two in Europe (the Europa League and the European Super Cup).
"I have to thank the fans; the support they have given me has been spectacular. I will continue to follow Atletico as a fan myself."
Simao completed his three and a half years at the Vicente Calderon by scoring the only goal of the game against Espanyol in Atletico's Copa del Rey clash on Wednesday night.