The Mexican will replace Mauricio Pochettino, who was let go earlier in the day after leading the club to a last-place spot through 13 games.
Espanyol sits in last place in La Liga after a 2-0 home defeat to Getafe on Sunday, picking up just nine points in 13 games this season.
Aguirre, who coached the Mexico national team on two separate occasions, last coached Real Zaragoza, a position he held until he was fired in December 2011. He has also coached Osasuna and Atletico Madrid in Spain in addition to guiding Atlante and Pachuca in Mexico.
Aguirre first coached Mexico from 2001-02 and again from 2009-10, when he resigned after the team failed to reach the quarterfinals of the World Cup in South Africa.
As a player, Aguirre was a midfielder for several Mexico clubs, including Club America, Guadalajara and Atlante. He also played one season in the NASL for the Los Angeles Aztecs and made 13 appearances for Spain's Osasuna.
It is reported that Aguirre's salary with Espanyol will be around $2 million per season.