No fee was announced but he is reportedly moving for 20 million pounds ($24.5 million).
"Serge Aurier, Davinson Sanchez and Victor Wanyama will return to Enfield to start pre-season training next week following commitments with their national teams at summer tournaments".
Once all the documents have been written, "AS" say the right back will sign his Atletico contract.
Arsenal are set to beat Tottenham to the signing of young French defensive star William Saliba, according to reports from France. However, two weeks ago Atletico sporting director Andrea Berta chose to step up negotiations for Trippier in a deal which could rise to around €30m with add-ons.
However, after agreeing a deal with Tottenham, Trippier arrived in Madrid on Wednesday where he underwent a medical before putting pen-to-paper on a three-year deal.
It's believed the England global would prefer a move to the north of England, closer to his South Yorkshire roots.
The Spanish club have also secured Joao Felix for £113m from Benfica and Marcos Llorente from Real Madrid, while selling Antoine Griezmann to the champions, Barcelona, for £107.7m. Atletico will pay around €25m for Spain worldwide, who will also sign a four-year-deal. It is an imperative condition should we come to an agreement on his transfer.
The England global has signed a 3-year contract at the Wanda Metropolitano, and it's believed he's cost Atleti £20m (€22.1m).
Atletico are also considering Napoli playmaker Fabian Ruiz as an alternative, but president Enrique Cerezo said on Tuesday the Rojiblancos are interested in James.
An source from Atletico told Reuters that negotiations were ongoing with Tottenham.