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.
"I thank Aguirre and I wish you all the luck in the world," he said.
"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."
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