"My cycle at River has finished," the former Lazio and Argentina midfielder, who had a contract until the end of the season next June, told a news conference.
"I'd like to return one day as coach or director.
"For me it was an honour to coach River, I have no regrets. Today I can leave River without lowering my head."
The 38-year-old Almeyda, who made his name in Italy's Serie A with Parma, Lazio and Inter Milan, said he felt he no longer had the support of most of the club's board and had reached agreement with president Daniel Passarella that a change of coach was needed.
Defending his record as coach, Almeyda said: "We fought with good football, played 60 matches, won 22 and lost nine in a year and a half with 100 goals for and 45 against.
"If you look at the numbers, it wasn't as bad as people imply."
Passarella, who has been a target of fans' frustrations during River's struggles, told reporters at evening practice that the decision for Almeyda to step aside was mutual and for the good of the club.
Almeyda's successor would become the fifth coach under Passarella since he won the club chair at the end of 2009.
