The 46-year-old replaces Manolo Gonzalez, who was sacked on Tuesday following Espanyol's shock 4-3 Copa del Rey defeat to fourth-tier Sestao.
Sarabia arrives after a successful spell at Elche, whom he guided to promotion to La Liga before keeping them in the top flight.
He previously worked as assistant manager to Quique Setien at Barcelona for seven months in 2020, gaining experience at one of Spain's biggest clubs.
Espanyol have confirmed that Sarabia's official presentation and first press conference will take place next Tuesday at the Juan Segura Palomares Auditorium.
However, he will not have much time to settle in, with his first match in charge coming against Villarreal on Friday.
Espanyol are 18th in the La Liga standings after 10 matches, having collected just eight points. Sarabia faces the immediate challenge of lifting the team away from the relegation zone and restoring confidence after their disappointing cup exit.