The 46-year-old, a Gijon native, played for the club for five years and took over as head coach in 2014.
However, he decided to resign from his position with the Asturias outfit 18th in the La Liga table after losing seven of their last eight league games.
Abelardo was entitled to a payout of €4m, but he waived it, stating: "[I] couldn't do that to the club I love."
He told reporters at a press conference: "I did the same at other clubs and it wasn't going to be any different here. I don't have a problem writing off the money. There are more important things, loyalty to my club above all."
Gijon president Javi Fernandez, meanwhile, said: "[Abelardo] has refused to take the club's money, including what he was entitled to for this season, as it was the only way we could bring in another coach. Our relationship will not change and he will always be in the hearts of Sporting fans."
The ex-Spain and Barcelona defender, who was in tears during the news conference, will be replaced by former Girona, Real Valladolid and Levante coach Rubi. body check tags ::