Over the course of 14 seasons he played in 296 La Liga games, in representation of four teams.
Born in São Paulo, Brazil, Biurrun was of Basque descent and moved to Spain at a young age. He started playing professionally with Real Sociedad (after appearing with the reserves his senior beginnings) but, blocked by Spanish international Luis Arconada, he was forced to move and joined Navarrese neighbours CA Osasuna, appearing in 60 La Liga games from 1983 to 1986.
After having joined another Basque club, Athletic Club de Bilbao, being deemed eligible to play for the Lions due to his roots, Biurrun established himself as a top flight player, with a further 151 league matches during four seasons. Subsequently he signed with RCD Español as a replacement for recently retired Thomas N'Kono, playing in 81 league matches during his tenure.
Biurrun retired in 1995 at nearly 36 years of age, after ending where he had started, Real Sociedad. He stayed connected with the game, as a players' advisor.
- Real Sociedad
- La cantera vasca llega hasta Brasil (The Basque cantera goes all the way to Brazil); El Mundo Deportivo, 7 December 1982 (Spanish)
- Voluntad de tradición (Will of tradition); El Correo Digital (Spanish)