The Mexican joined the Catalan outfit midway through the 2012-13 campaign and guided the club to a 13th-placed finish at the end of that term.
They have experienced a similar season this time around, currently lying 12th in La Liga with one match left to play, away to Real Madrid on Saturday.
It has been a disappointing end to the campaign, however, with Espanyol's last league win coming against Malaga on March 25.
In a press conference on Friday, club president Joan Collet confirmed the announcement.
"I thank Aguirre and I wish you all the luck in the world," he said.
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."
