The 55-year-old Aguirre, who coached Mexico at the 2002 and 2010 World Cups and was in charge of La Liga side Espanyol last season, will come to Japan in the middle of August to formally sign the deal, Kyodo news agency said.
The financial terms and the length of the deal were not disclosed.
Zaccheroni's four-year spell in charge of the Asian champions ended last in Brazil when Japan finished bottom of their World Cup group, falling short of the Italian's ambition to take them to a first quarter-final.
The team's dismal World Cup campaign ended with a 4-1 defeat by Colombia after an opening loss to Ivory Coast and a 0-0 draw with 10-man Greece.
Aguirre, a former midfielder nicknamed "El Vasco" (Basque) who helped Mexico reach the quarter-finals when they hosted the tournament in 1986, steered his country to the last 16 on both World Cup appearances as their coach.
He has also coached Atletico Madrid, Osasuna and Real Zaragoza in Spain.
Japan will play two friendlies at home in September against Uruguay and Venezuela but Aguirre's first major assignment will be when the Blue Samurais defend their Asian Cup title in Australia in January.
(Reporting by Sudipto Ganguly; editing by Rex Gowar)
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