Sarabia replaces Manolo Gonzalez, who was sacked on Tuesday after a 4-3 Copa del Rey loss to fourth-tier Sestao.
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The 46-year-old was most recently in charge of Elche, guiding them to promotion and then survival in LaLiga in two seasons.
Sarabia spent seven months as assistant manager to Quique Setien at city rivals Barcelona in 2020.
Espanyol face Villarreal on Friday on Sarabia's debut as manager.
After 10 games, Espanyol are 18th in the LaLiga standings with eight points.