The 28-year-old inked a three-year contract with Los Colchoneros and will fill the void left by legendary right-back Juanfran, who departed at the end of the 2018-19 campaign.
Trippier also represents the capital club's third major defensive acquisition of the summer after center-back Felipe joined from FC Porto and left-back Renan Lodi was tempted from Brazilian outfit Athletico Paranaense.
Atleti's latest arrival follows a season of indifferent form for Spurs. Trippier was a standout player for England during its run to the 2018 World Cup semifinals, but looked susceptible at the back upon his return to club football.
Given his new manager Diego Simeone's dedication to regimented defensive play, Trippier could have a few tough months of training ahead of him. Alvaro Morata and his other attacking colleagues in Madrid, meanwhile, will hope to be regular beneficiaries of Trippier's trademark devilish deliveries from the right flank.
Trippier moved to Spurs in 2015 from Burnley. After initially failing to make the grade at Manchester City, the full-back has appeared 107 times in the Premier League and represented his country on 16 occasions.