Corica was appointed Auckland's inaugural coach for the 2024/25 season.
Auckland captured the league's most coveted piece of silverware in their second season with an ironic 1-0 triumph over Sydney FC, the club that sacked Corica as head coach in 2023.
The victory in May marked the first time a New Zealand club had won an A-League grand final.
Corica replaces Hideo Oshima, who took charge of Yokohama in June last year but was dismissed this month after the club finished seventh in Group A of the J1 League.
In the past eight years, fellow Australians Ange Postecoglou, Kevin Muscat, Harry Kewell and Patrick Kisnorbo have had stints coaching the Japanese powerhouse.
Postecoglou and Muscat both delivered trophies and earned the attention of clubs from around the world, while Kewell (seven months) and Kisnorbo (two months) were swiftly sacked.
It is a return of sorts for Corica, who played for Japanese outfit Sanfrecce Hiroshima in 2000-2001.
"I am incredibly proud and honoured to be returning to Japan," the 53-year-old said in a statement.
"My first experience here was as a player, and now to come back as manager of such a fantastic football club is a privilege that means a great deal to me.
"Yokohama F Marinos is a club with a proud history and high expectations.
"I have come here with a clear ambition – to win trophies, restore a winning mentality and re-establish the culture and standards that have made this club one of the most successful in Japan."
Corica vowed his team would play "exciting football" and "compete for titles".
The former midfielder played 32 games for the Socceroos before becoming a Sydney FC figurehead, as captain then coach.
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