The Spanish-Argentine defender, 19, has signed a contract at the Metropolitano running until 2031 after Atlético paid a release clause in excess of one million euros to prise him away from Butarque.
The move represents the largest sum Leganés have received for a graduate of their academy who had not yet made an official debut for the first team, though the timing and manner of the deal, arriving on deadline day itself, was not well received inside the club.
Auguste joined Leganés as a youth player after arriving from Argentine side Aravaca CF, progressing through the club's junior categories before making the step up to the reserve side while still a teenager.
He impressed sufficiently during pre-season under head coach Rubén Albés to be included in the matchday squads for both of Leganés's opening two league fixtures this season, against Girona and Real Oviedo, without making his senior debut.
Standing 1.90 metres and playing as a left-footed centre-back, Auguste had been considered one of the more promising prospects in Leganés's academy system, prized for his composure in possession and reading of the game as much as his physical profile.
Losing a player of his potential represents a blow to the club's long-term planning, even accounting for the financial windfall his release clause has generated.
Atletico Madrid's interest reflects their continued strategy of identifying young defensive talent from lower-tier academies across Spain before they attract wider attention. Auguste now joins a club with considerably greater resources and a well-established pathway for developing central defenders, giving him the platform to continue his progression at a significantly higher level than Segunda Division football with Leganés could have offered.
The deal is likely to sting at Butarque given how close Auguste had come to a first-team debut, having trained consistently with Albés's senior squad throughout pre-season.
Leganés, who are managing their own promotion push in the second tier this season, will now need to identify the next graduate capable of stepping into a similar role, with the compensation received offering some financial cushion but doing little to soften the loss of a player many inside the club believed had a genuine future at the highest level of Spanish football.