Zaccheroni's four-year spell in charge of the Asian champions ended last week after Japan finished bottom of their World Cup group, falling short of the Italian's ambition to take them to a first quarter-final.
A lack of physicality had been blamed for Japan's poor showing in Brazil, with Kyodo saying that JFA technical director Harumi Hara had wanted the new manager to replicate the swift, successful passing styles of the generally diminutive Spanish and Mexican teams, who were of similar size to the Japanese.
Aguirre took Mexico to the last 16 on both World Cup appearances and has also coached Atletico Madrid, Osasuna and Real Zaragoza in Spain.
Japan will defend their Asian Cup title in Australia in January.
(Reporting by Patrick Johnston; editing by Justin Palmer)
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