The 54-year-old, in his third spell in charge of the club, guided the team to the Argentinian championship on Sunday with a 1-0 win over San Lorenzo in the final.
Diaz also spent five years over two spells at River as a player in the 1970s, 80s and 90s, and his departure was confirmed in a statement on the club's official website on Tuesday.
"The club Atletico River Plate reports that the president of the institution, Rodolfo D'Onofrio; vice president, Matias Patanian; and the technical secretary, Enzo Francescoli, met with Ramon Diaz, who was accompanied by his son Emiliano and his representative.
"At the meeting, the coach said he had served its purpose, which is why he made the decision to disengage from the club.
"Moreover, it is reported that Gustavo Zapata and his coaching staff will assume interim basis driving the professional staff."
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