The right-back signed a three-year contract in the Spanish capital on Wednesday, bringing an end to his four-season stint at Spurs.
Trippier, 28, has the chance to rediscover the form that eluded him last season as he forges a place in Diego Simeone's notoriously mean defence.
"The Premier League is one of the best leagues in the world, but I didn't think twice when Atletico were interested," Trippier said at Thursday's presentation.
"It's a great opportunity to come and live in Madrid. Not many British players come abroad, but I always wanted to play abroad, especially in La Liga, since I was young.
"I'm looking forward to learning the language straight away, which is my first priority. The quicker I can do that, communicate with my coach and team-mates, the better.
"I want to enjoy playing for Atletico and living in Madrid."
Trippier greeted the local media moments after Atletico sealed the signing of another defender, centre-back Mario Hermoso.
The Spain international, formerly of rivals Real Madrid, arrives from Espanyol in a €29 million (£26m/$33m) deal.
If starting his career across town does not attach enough pressure, Hermoso also has the unenviable task of trying to plug the gap left by Diego Godin's departure for Inter.
"It's a beautiful, important challenge," the 24-year-old said.
"Diego has been a symbol for the club. What better way to continue making history. I hope to continue that line."
Atletico have gone through a summer of change, which has seen mainstays Antoine Griezmann, Diego Godin, Lucas Hernandez and Juanfran depart, but Joao Felix, Trippier, Hermoso, Hector Herrera and Marcos Llorente among those who have arrived.
The club will face Numancia in a friendly Saturday before playing their International Champions Cup slate against Chivas and local rivals Real Madrid, and a match against the MLS All-Stars to close out July.