Born in Zarautz, Gipuzkoa, Basque Country to an Algerian father and a Spanish mother,[4] Berchiche started his career in the cantera of Real Sociedad, but left for rivals Athletic Bilbao at the age of 16.

[7] In April 2009, Berchiche made a robust tackle on Scunthorpe United's Henri Lansbury (on loan from Arsenal), leaving his opponent with a suspected broken leg.

[15] In June, after helping Eibar obtain promotion to the top flight for the first time in its history, he was selected by the Liga Nacional de Fútbol Profesional to its starting XI.

[24] Berchiche played 32 competitive matches in his only season,[25] winning three trophies including the national championship and the Coupe de France, defeating amateurs Les Herbiers VF 2–0 in the final of the latter tournament.

[30] On 5 March 2020, Berchiche scored late in the semi-final second leg of the Copa del Rey against Granada CF and enabled his team to progress on the away goals rule.

[31] In addition to the decisive game, which was delayed until April 2021 by the COVID-19 pandemic in Spain, they also qualified for the 2020–21 Supercopa de España which they won by beating FC Barcelona;[32] however, he was unable to take part in those matches due to a thigh injury sustained against the same opposition a few weeks earlier.

[35] That proved to be the player's last appearance of the campaign due to a persistent pubalgia issue which light treatment failed to cure, and an operation was carried out in July with an estimated recovery time of three months – manager Marcelino García Toral expressed his frustration at the delay in the injury being dealt with.