Bosz joined in the summer after guiding Ajax to the final of the Europa League, but leaves with the Schwarzgelben seventh in the Bundesliga table.
Saturday's 2-1 defeat at home to Werder Bremen left Dortmund without a win in 12 games in all competitions and three points adrift of a Champions League place.
Club chief executive Hans-Joachim Watzke said in a statement: "Last night, in a conversation with Peter Bosz, we decided that we would release him with immediate effect.
"It was very emotional, but also respectful. On behalf of all at Borussia, I would like to thank Peter Bosz. We still consider him a great coach and person."
Dortmund also announced that Stoger, who left Koln earlier this month, would take charge of the team until the end of the season.
The 51-year-old enjoyed a four-year tenure at Koln in which he guided them to promotion from the second tier and to fifth place in the league last season to earn European football.
Stoger is due to oversee his first training session later on Sunday, with his first match coming on Tuesday night, away to Mainz 05.