Sabella, who took over in 2011, has led Argentina to their first World Cup final in 24 years, where they will face a powerful German side that demolished hosts Brazil in the semi-finals on Tuesday.
While Argentina will now have to step up the search for a successor, Sabella could deliver no better parting gift than winning the World Cup on the soil of their fiercest rivals.
Former Barcelona coach Gerardo Martino and Atletico Madrid's Diego Simeone are being mentioned as possible candidates to replace the 59-year-old, according to media reports.
"To go at the top is always positive. I believe he gave everything to the national team and that now is the time to give way to another person," Eugenio Lopez told FM Delta.
"He's going. He's leaving whatever happens. Whether they are champions or not, a cycle is ending."
While state news agency Telam said the 59-year-old's contract was due to expire after the tournament, the news caught some by surprise in Argentina.
"It's not good that the announcement came before the final. Psychologically it is not good for the players," said soccer enthusiast Facundo, declining to give his surname.
"He did something no trainer had done in years, which was to make a group of players play as a team. So as a fan of Argentine football, I wish he would carry on, regardless of whether we win or lose."
Sabella told Argentina sports newspaper Ole that he was focused only on Sunday's match.
"The future, for me, is the next match, the World Cup final. Thinking about something different would be disrespectful," he said.
Argentina have been more workmanlike than wonderful under Sabella, despite the presence of four-times World Player of the Year Lionel Messi, but he has forged a formidable work ethic in the side and introduced much-needed tactical discipline.
Their win over Belgium equalled Argentina's longest World Cup winning streak at five games, though they needed a penalty shootout to see off the Netherlands in the semi-final in Sao Paulo on Wednesday.
Sabella, capped eight times by Argentina, left River Plate in 1978 to play in England with Sheffield United and Leeds United before playing for various club sides back home as well as in Brazil and Mexico.
After retiring from the playing side in 1989, he worked beside ex-Argentina defender Daniel Passarella at the Uruguay national team and at Parma in Italy, and was part of the Argentina set-up at the 1998 World Cup.
He got his first head coaching job in 2009 at Estudiantes and led them to their fourth Copa Libertadores title.
Two years later he was put in charge of Argentina, World Cup champions in 1978 and 1986 but who had not reached the final since 1990.