In 1994, he signed with Argentine Primera División giants River Plate where he was dubbed Mono (monkey) because of his height and disheveled appearance,[3] going on to win several titles during his spell, notably the 1994 Apertura where his team did not lose one single match.

On 27 November 1999, he was suspended for eleven games for punching Espanyol player Manolo Serrano in a match played the previous week, in an action that eluded the referee but was caught on camera.

[11] Burgos was the starter in the latter half of the qualifying campaign for the 2002 World Cup (unseating Roberto Bonano) and it was generally expected that he would be the first choice in the finals,[12] but manager Marcelo Bielsa ultimately chose Cavallero.

[19] Burgos was handed his first job as a head coach at the professional level on 14 March 2021, when he signed a contract until the end of the year at Newell's Old Boys with the option to renew it for a further season.

[20][21] He joined midway through the Copa de la Liga Profesional, and his side earned ten points from their remaining eight games, finishing bottom of Zone B.

[28] On 11 April 2024, Burgos was let go from his position as a sports commentator for Spanish TV broadcaster Movistar Plus+ for controversial remarks about Barcelona player Lamine Yamal.