Born in Abadiño, Biscay, Iturraspe joined Athletic Bilbao in 1999, at the age of 10; he returned to his hometown four years later due to homesickness, but went back to Lezama to complete his development shortly after.

[8] He made his La Liga debut on 14 September, starting in a 0–0 draw at Málaga CF in the same match as another youth graduate, Mikel Balenziaga;[9] his second appearance came as a substitute, in the 2–0 home victory over Real Valladolid.

Benefitting from physical problems to veteran Carlos Gurpegui, Iturraspe played 58 official games in 2011–12 under new manager Marcelo Bielsa; Athletic reached both the UEFA Europa League and the domestic cup finals.

The club's final home match involved tributes to him, as well as fellow long-serving squad members Mikel Rico and Markel Susaeta who were also departing in similar circumstances.

[12] Following a strong 2013–14 season, Iturraspe was called up by Spain national team manager Vicente Del Bosque to his 30-man provisional squad for the 2014 FIFA World Cup,[21] making his debut on 30 May in a friendly with Bolivia in Seville[22] where he played the full 90 minutes (2–0 win).