The Argentina defender, who joined Spurs in 2021 and was appointed captain last year, posted a message on social media thanking the club and fans after five seasons in North London.
"I leave with a heart full of memories and enormous pride for everything we lived and achieved together," Romero wrote.
Romero helped Tottenham win the 2024/25 Europa League, their first trophy since 2008, and was named the competition's Player of the Season by UEFA.
Tottenham have agreed a deal with Atletico worth around 40 million euros ($46.26 million), including add-ons, according to reports.
"Once I was one of you. Today, I leave as one of you forever," Romero wrote.