The 52-year-old's final match in charge was Saturday's 3-1 loss to Hoffenheim, which left the Die Borussen hanging on for fourth place.
BVB finished level on points with two other sides after the final round of fixtures, but secured a Champions League spot thanks to a superior goal difference over fifth-placed Bayer Leverkusen.
Stoger only replaced Peter Bosz as head coach in December, and he is happy to have guided Dortmund from eighth place up to fourth during his short time in charge.
"Today was my final competitive game for Dortmund," he told reporters after the game. "We already decided that together some time ago. We decided that a new stimulus is necessary and might do the club good. The easiest way to get that is with a new coach.
"I'm happy that we achieved our most important goal. I hope that my successor can bring a bit more stability and serenity to the team."
Dortmund have now qualified for the Champions League in six of the last seven seasons.