Spurs retain a 15 per cent sell-on clause as part of the deal that has seen him pen a five-year deal.
Atletico have been long-term admirers of the Argentina international, and there was an expectation that Spurs would allow Romero to depart this summer if the right offer arrived.
The central defender was always believed to have preferred a move to Atletico, with Inter Milan and Spurs' north London rivals Arsenal among the other clubs to have been interested.
Romero's Spurs deal was due to run until the summer of 2029.
The 28-year-old was sent off twice last season during Spurs' Premier League relegation battle. He then missed the end of the campaign due to a knee injury.
Romero received criticism from supporters when he appeared to be set to watch his boyhood club Belgrano play River Plate in the Argentina Primera Division Apertura final instead of being at Tottenham's crucial last game against Everton. However, he did ultimately attend the game.
In a post on Instagram, Romero bid farewell to the fans on Friday and said he had achieved his dream of leaving his name in the club's history as the captain of the side that ended Spurs' 17-year trophy drought.
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"Today, I say goodbye to a place that, for five seasons, was much more than a club. It was my home, my challenge and the place where my family and I built such an important part of our lives.
"I leave with a heart full of memories and enormous pride for everything we lived and achieved together.
"When I arrived, I had a clear dream: to leave my name in this club's history. I knew the only way was through hard work, sacrifice and achieving something that had seemed so difficult for so long: lifting a trophy again. And we did it.
"The journey wasn't perfect, but I don't want that to define my goodbye. I choose to remember the happy moments, the lessons, the people who stood by me and, above all, the love I received during these five years.
"Thank you to everyone at the club who shared this journey with me. Coaches, team-mates, staff and every person working behind the scenes you are all part of my story and have a place in my heart."
Will Spurs fans miss Romero?
Sky Sports News' Michael Bridge:
"No.
"Even announcing the move before the club have announced it, it's Romero.
"On his day he was one of the best centre-backs in the world but those days came against Ecuador, Peru on international duty.
"There's nothing wrong with being proud to play for your nation but there was too many times it was a chore playing for Spurs.
"He posted a few public comments about the board, which you can't do. He was a key part of winning the Europa League but there was that final day saga about whether will he or won't he watch his team try to avoid relegation.
"The time was right for him to move."
