The Mexican joined the Catalan outfit midway through the 2012-13 campaign and guided the club to a 13th-placed finish in his first season.
They have experienced a similar capaign this time around and currently sit 12th in La Liga ahead of their final match of the season this weekend when they visit Real Madrid on Saturday.
"I thank Aguirre and I wish you all the luck in the world," Club president Joan Collet told a press conference on Friday.
Aguirre, meanwhile, took time to thank the supporters, with Espanyol still to contest the Copa Catalunya final against Barcelona after the conclusion of their league season.
"We decided to put an end to this stage," he said. "It's the best possible decision.
"I thank everyone involved in the club for their support. I thank the fans who have helped us a lot. I want to win both remaining games."
Espanyol's last league win coming against Malaga on March 25.