Trippier will be the first English player to play for Atletico in La Liga and the third British player in Spain's top flight next season alongside Scottish forward Jack Harper of Getafe and Real Madrid's Gareth Bale.
The man who was the first choice for England in the 2018 World Cup finals may not be the only arrival at Atletico this week with the side that finished behind FC Barcelona in last season's Liga Santander expected to seal a deal for Espanyol's Spain global central defender Mario Hermoso for a similar fee.
Coach Diego Simeone has also forked out 126 million euros for Portugese teenager Joao Felix this summer.
Atletico said the 24-year-old had signed a five-year deal.
"The support you've shown me and the team took us to new heights, and with the new stadium I have no doubt that the team and fans have many exciting times ahead!"
"For me, he's one of the best managers in the world and it's an absolute privilege to play for him and give everything I can for him".
In France, Paris Saint-Germain added Ander Herrera, Pablo Sarabia and Abdou Diallo to their squad, while Premier League champions Manchester City signed Rodrigo Hernandez from Atletico and Angelino from PSV Eindhoven.
And it would seem having the opportunity to work with Simeone was a major factor in Trippier's move to Madrid.
The former Burnley full-back will become the first English player to play for Atletico in nearly 100 years. I've always wanted to play overseas, especially in LaLiga.
He joined Spurs from Burnley in 2015 and made 114 appearances for the London club.
'Something that I can't wait to do is work with the manager, learn from the manager and help the team to be a success in the future.