Some of the notable accomplishments under Alguacil's leadership include winning the Copa del Rey title and qualifying for the European competitions five times, with the possibility of securing a sixth qualification at the end of this season.
Back in a few months, Alguacil had mentioned that he received an offer to extend his contract with Real Sociedad, and he planned to make a decision by the end of April or early May.
Alguacil's departure comes at a challenging time for the team, as they face difficulties in achieving their goal of qualifying for a sixth European competition this season.
Real Sociedad's other objectives for the current season were to reach the Copa del Rey final and advance in the Europa League, where they were unfortunately eliminated by Manchester United in the round of 16.
Throughout his time at Real Sociedad, Alguacil has coached a total of 334 matches, making him the third highest in the club's history, behind Benito Díaz and John Benjamin Toshack.