Mendilibar was relieved of his duties on Monday following Sevilla’s poor start to the new season.
Despite leading Los Nervionenses to the Europa League title last term, the 62-year-old guided the team to just two victories in eight league games.
The Andalusian outfit have wasted no time in appointing his successor, handing over the reins to Alonso.
The former Uruguayan striker has spent most of his managerial career on the American continent, with some notable stints at Monterrey, Pachuca and Inter Miami.
The 48-year-old had twice won the CONCACAF Champions League as a manager with Monterrey and Pachuca.
However, with Uruguay failing to progress to the knockout stage, Alonso immediately stepped down from the coaching role.
Sevilla will be his first job in Europe, although he has fond memories in Spain, having represented Atletico Madrid, Valencia and Malaga during his playing days.
Alonso is Sevilla’s third managerial appointment in a year, and he faces a big task to bail the Andalusians out of their difficult situation.
The Uruguayan’s first game will be against Real Madrid after the international break before facing Arsenal in the Champions League.
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