Almeyda spent one season at Sevilla when he joined from River Plate in 1996, before moving on to play with Lazio, Parma and Inter Milan in Italy. After ending his playing days back at River Plate, he began his managerial career there.
The 51-year-old spent the last two seasons in charge at Greek club AEK Athens, where he won the domestic double in his first campaign, having earlier parted ways with San Jose Earthquakes in the MLS.
Sevilla avoided relegation by one point last season, with manager Garcia Pimienta sacked in April and Joaquin Caparros appointed until the end of the season, a campaign which saw angry fans storm the club's training ground last month.