Burgos made his debut in the main category on 27 August 2014, starting in a 1–0 away win against Rosario Central.[5] After featuring sparingly, he moved to the latter club on 5 January 2016, on an 18-month loan deal.[6]
Alcorcón
On 7 July 2017 Burgos moved abroad for the first time in his career, after agreeing to a two-year deal with Segunda División side AD Alcorcón.[7] He made his debut for the club on 19 August, starting in a 0–0 home draw against Sporting de Gijón.
Eibar
On 1 July 2019, free agent Burgos joined La Liga side SD Eibar, signing a three-year deal.[8] He made his debut in the category on 14 December, replacing injured Pedro Bigas in a 0–0 away draw against Athletic Bilbao, and scored his first goal the following 18 January, netting the opener in a 2–0 home win over Atlético Madrid.
Málaga
On 15 July 2022, Burgos signed a two-year contract with Málaga CF in the second division.[9] On 30 June of the following year, after the club's relegation, he left after activating an exit clause on his contract.[10]