In October 2010 he joined Segunda División B club Terrassa FC, in order to help him gain a Spanish passport to ease a potential move to a higher-rank team within Europe.
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Aguirregaray made his professional debut in 2007 with a Peñarol shirt, and spent four full seasons with the club.
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On 24 August 2011, Serie A club Palermo confirmed to have signed Aguirregaray on loan from Montevideo Wanderers F.C., with an option to fully acquire the player's transfer right by the end of the season.
Matías Ruiz | José Matías Delgado | Vicente Matías Vuoso | Sónia Matias | Order of José Matías Delgado | Matías Soto | Matías Romero | Matias Loppi | Matias Köykkä | Matias Duarte | Matías Díaz | Matias Corporation | Matías Córdoba |