Costa played in the youth ranks of River Plate de Montevideo.

Costa signed for Bella Vista in 2012, where he made his debut in the Uruguayan First Division under manager Guillermo Sanguinetti.

[4] In July 2024, he switched to Universitario,[5] becoming one of the few players who have played for the Big Three of Peruvian football clubs.

[6] Born in Uruguay, Costa was nationalized after years in Peru and gained a Peruvian passport.

[7] He debuted for the Peru national team in a friendly 1–0 loss to Ecuador on 6 September 2019.