Flores last managed Getafe, where he was dismissed after the club fell into the relegation zone. The Spaniard has also had spells at English side Watford, Espanyol, Atletico Madrid, Benfica and Valencia, among others.
"Sevilla FC and Quique Sanchez Flores have reached an agreement for the coach to become the new coach of the first team, signing until 2025," Sevilla said in a statement.
Sevilla sacked Alonso on Saturday after he managed just two wins since his appointment in October when he replaced Jose Luis Mendilibar.
The Uruguayan had failed to win a game in the league or in European competition during his nine-week stint, leaving the club reeling in 16th place in the Spanish top flight.
Sevilla, now 17th, next visit fellow strugglers Granada in the league on Tuesday.
