The 33-year-old, who played for Chelsea under compatriot Jose Mourinho in the 2004-05 season, became a free agent in June and was reportedly prepared to move back to Stamford Bridge while entertaining various rival offers from around the world.
But Tiago has instead committed to Atletico - the Champions League runners-up in May - after signing a new deal and flying out to their pre-season training camp in Segovia.
Speaking to the club's official website, he said: "The club offered me the chance to renew my contract.
"I felt proud because we had had an incredible season, but I had thought it was the right time for the cycle to come to an end.
"I have been offered the chance to play in various international leagues and have taken some time to evaluate my options during the summer, but my final decision became clearer, and Atletico was the only option."
Aside from contributing to Atletico's remarkable run to the Champions League final, Tiago has won the Primera Division title, the Europa League and the Copa del Rey with Diego Simeone's Rojiblancos.
He also boasts a Premier League winner's medal from his year with the Blues.
"El Cholo (Simeone) always left the door open for me and I am now very happy that I have made the right decision," Tiago added.
"I want to thank the club for waiting for me and offering me the opportunity to remain here.
"I can't wait to help out in any way I possibly can."