[2] A youth academy graduate of Peñarol, Álvarez made his professional debut on 13 September 2020 in goalless draw against Montevideo City Torque.
[5] On 17 June 2022, Álvarez joined Serie A club Sassuolo on a five-year deal.
[7] On 18 January 2024, Álvarez moved to Sampdoria in Serie B on loan until the end of the season.
[8] On 17 August, he moved to Spanish Segunda División side Elche also on loan.
[10] On 29 August 2021, he received his first call-up to senior team for FIFA World Cup qualifiers.