Aguirregaray made his professional debut in 2007 with
Peñarol and spent four full seasons with the club. In October 2010 he joined
Tercera División club
Terrassa FC, in order to help him gain a Spanish passport to ease a potential move to a higher-rank team within Europe. He never played a single game with the Catalans. 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. He made his debut as a second-half substitute for
Nicolás Bertolo in a Serie A home game against
Cagliari, ended in a 3–2 win for his side. In July 2013 he signed a contract with
Argentine club
Estudiantes de La Plata. ==International career==