The experienced Esnal, known as Mane in Spain, replaced Bartolome 'Tintin' Marquez at the beginning of last month but his only victory since then was an away goals win against Segunda B (third tier) side Poli Ejido in the King's Cup.
The Barcelona-based club were beaten 4-0 by Malaga on Sunday in the Primera Liga and are in 18th on 20 in the standings with only three wins all season.
"After a long meeting which continued into the early hours of the morning, and after analysing the sporting situation of the team, the management decided the coach should end his duties," the club said on its website.
Pochettino would be presented to the media and afterwards take charge of his first training session, it added.
His first match as coach will be on Wednesday at home to league leaders and city rivals Barcelona in the first leg of their King's Cup quarter-final.
The 36-year-old had two spells as a player with Espanyol, ending his career in June 2006. He also played for Newell's Old Boys, Paris St Germain and Girondins Bordeaux and was a member of the Argentina squad at the World Cup finals in 2002.
Mane made his name with Alaves when he led them into the top flight in 1998 and then to the final of the 2001 UEFA Cup, where they lost 5-4 to Liverpool on a golden goal.
"Mane did not provide the positive catalyst for change that we were expecting," El Pais newspaper quoted Espanyol official Joan Collet as saying on its website.
