Atletico said on their website they had signed a "fantastic and experienced player from the Champions League runner up" and added Trippier had agreed a three-year deal.
Spanish and British media said Atletico were paying Spurs a fee of €22 million.
Trippier has played 16 times for England scoring one goal, direct from a free kick in the World Cup semi-final loss to Croatia last year.
He joined Spurs from Burnley in 2015 and made 114 appearances for the London club.
The signing continues an overhaul of the capital city outfit's backline.
Defenders Diego Godin, Filipe Luis and Lucas Hernandez have left, while Brazilian pair Renan Lodi and Felipe has already signed.
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