The Europa League holders sacked Jose Luis Mendilibar earlier this week following an underwhelming start to the season.
The Andalusian side have started the domestic campaign with four defeats and just two wins from their eight games played so far.
Sevilla have also drawn their opening two Champions League games against Lens and PSV Eindhoven.
Sevilla currently lie 14th on the Spanish La Liga table following a hard fought 2-2 draw with Rayo Vallecano on Saturday.
Alonso was without a club after getting sacked by Uruguay after their group stage exit at the 2022 FIFA World Cup in Qatar.
The 48-year-old former Uruguay striker spent a significant chunk of his playing career in Spain, turning out for the likes of Racing Santander, Atletico Madrid, Valencia, Malaga and Real Murcia.
A club statement read: "We are delighted to announce that Diego Alonso has reached an agreement for the Uruguayan to become our new coach until the end of the current season.
Alonso's first two games in charge of Sevilla will be against Real Madrid in La Liga and Arsenal in the Champions League.
