Aguirre took charge of the Spanish outfit in November 2013 when they were bottom of La Liga, but led the club to safety and was expected to continue into the new season.
However, the Mexican sought pastures new at the end of the campaign, taking charge of the Japan national team after the World Cup.
"Contact was first made in 2010. After that World Cup [in South Africa] the Japanese FA sought me out, but at that point my youngest son was still at school and we couldn't leave Spain," he told FIFA.com.
"Then, four years later, they revived their interest after I'd already told Espanyol I wouldn't be staying. Signing a new contract would have been difficult because there was hardly any money to strengthen the squad, so I decided to step aside.
"I had a few offers to stay in Europe but I wanted to broaden my horizons – and that's when Japan came back on the scene."
Aguirre replaced Alberto Zaccheroni at the helm of Japan.