The Portuguese midfielder had been linked with a return to Chelsea this summer after coming to the end of his deal with the Spanish champions, but has elected to remain with the La Liga side.
The 33-year-old told the club's website: "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."
Tiago has won the La Liga title, Europa League and Copa del Rey during his spell with the club, as well as reaching the Champions League final earlier this year.