"My cycle at River has finished," said the former Argentina international, who had a contract until the end of the season next June. "I'd like to return one day as coach or director."
The 38-year-old Almeyda said he had reached agreement with club president Daniel Passarella that River needed a change of coach and that he had perceived he no longer enjoyed the support of most of the club's board.
Almeyda, a River player when they were relegated for the first time last year, took the reins and steered them back into the first division winning the Primera B Nacional second division title in June.
River, who hold a record 33 Argentine league titles, have struggled in the first division and Almeyda leaves them in mid-table with 23 points from 17 matches, 12 points behind leaders and title favourites Velez Sarsfield.