The Spanish side confirmed that the 28-year-old has joined on a three-year contract.
“We welcome Trippier to the Atleti Family and wish him the best of luck at his new home,” the club said in a statement.
The England international made 27 league appearances for Spurs last season – and 69 in total during his time in north London - as they finished in the top four and reached the Champions League final.
The right-back was briefly targeted by Manchester United after his heroics at the World Cup, scoring England’s only goal in the 2-1 semi-final defeat by Croatia.
It is not thought that Tottenham will look to replace Trippier during this transfer window, with Serge Aurier and the highly-rated youngster Kyle Walker-Peters believed to offer adequate depth.
Trippier’s arrival takes Atletico Madrid’s summer spending to close to £200m after they spent big on Joao Felix, as well as defenders Marcos Llorente, Felipe and Renan Lodi.