It was announced on Tuesday that Rueda would not be continuing in his role following a disappointing World Cup campaign.
Ecuador were eliminated in the group stages of the competition after taking four points from their three games, finishing third in Group E behind France and Switzerland.
Under-20s coach Sixto Vizuete is to take Rueda's place on an interim basis but, despite the Ecuador Football Federation's decision (FEF), Rueda was quick to express his gratitude to the governing body.
"I want to thank (FEF) president Luis Gustavo Chiriboga, officials, employees and others who are part of the family of the federation, for their generosity, support and loyalty in all the times we shared," Rueda said on the FEF's official website.
"Likewise, I extend my thanks to the president of the republic and all those Ecuadorians of heart, whether they be leaders, coaches, soccer players, personalities of various social and institutional levels, media, fans and people in general, who believed and supported their team, who wept after every defeat and rejoiced in every win.
"To all of them thank you very much, because without your support and your encouragement it would not have been possible to go to Brazil 2014.
"Best wishes to this group of players to continue at international level and achieve a new position in the highest echelons of world football."
Vizuete will continue in his temporary role until January 9, 2015, when the FEF is to hold a presidential election.