"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.
Almeyda took over at River in the wake of their first relegation in their 111-year history, and steered them back into the first division with the Primera B Nacional second division title a year later.
Almeyda appeared out of his depth in the top flight, however, constantly tinkering with his team and tactics, but was also unlucky to lose four players to serious knee injuries.
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."
River, who hold a record 33 Argentine league titles, are mid-table with 23 points from 17 matches, seven points short of their target for the championship.
They are 12 points behind leaders Velez Sarsfield, favourites to win the first of two championships in the season.
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.
Former striker and coach Ramon Diaz, who led River to seven domestic and regional titles between 1996 and 2002, was among three or four candidates, Passarella said.
River are at home to second-placed Lanus, who are two points behind Velez and the only team with a realistic chance of pipping them to the Inicial title.
Former player and Argentina midfielder Gustavo Zapata will take over River as caretaker coach.
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