"He did a sidestep yesterday but today he phoned (club president Ruben) Filipas and said he was leaving," the club's press officer Diego Raimundo said.
Sabella, who steered Estudiantes to their fourth Libertadores Cup in 2009 and the Argentine Apertura title in December, had given himself time to reconsider having told the club and players on Wednesday that he was quitting.
The former midfielder, who helped Estudiantes win two league titles in the early 1980s, gave no reasons for his decision.
Media said Sabella was unhappy Estudiantes had not heeded his request to sign another defender and striker to strengthen his squad to defend the league title and play this year's Libertadores.
"He didn't say anything and (captain Juan Sebastian) Veron hasn't spoken either," Raimundo said.
Raimundo also said Estudiantes had given no indication of who might succeed the 55-year-old Sabella in the job with their opening match of the Clausura championship, second of the 2010/11 season, at home to Newell's Old Boys on February 11.
Sabella, who was former Argentina coach Daniel Passarella's assistant at the 1998 World Cup in France, was linked with the national team job when Diego Maradona was told he was no longer wanted after the 2010 finals in South Africa.
A quiet man nicknamed "Sloth", he had impressed in his short spell in charge of Estudiantes, having taken over in March 2009 when they were midway through their Libertadores Cup campaign.
The team remained unbeaten under Sabella as they went on to add the crown the club's previous three South American titles from 1968-70.
Under Sabella, Estudiantes were also runners-up in the Argentine Clausura in the first half of last year and the 2009 Club World Cup.
Sabella, capped four times by Argentina, began his playing career at River Plate before spells in England with Sheffield United and Leeds United.
