Bosz arrived in the summer after guiding Ajax to the final of the Europa League but the 54-year-old Dutchman leaves with Dortmund seventh in the Bundesliga.
"In a conversation with Peter Bosz, we decided that we would release him with immediate effect," said Dortmund chief executive Hans-Joachim Watzke. "We parted on the best of terms and on behalf of all Borussia I would like to thank Peter Bosz. We still consider him a great coach and person."
Dortmund have failed to win a league game since September and lost 2-1 at home on Saturday to Werder Bremen.
There had been no consolation in the Uefa Champions League either for the fervent Dortmund faithful. The side - boasting a cluster of internationals - did not win any of their matches and scrambled two draws against APOEL Nicosia only advancing to the Europa League because they had let in fewer goals than the Cypriots.
Stoger, 51, was sacked by Cologne after failing to inspire the team in their second season in the top flight.
In their first campaign after promotion, they finished fifth and entered the 2017/2018 Europa League. But they have been eliminated from the competition after winning only two of their six games in Group H.
While there were creditable performances in Europe, they have been abject in the Bundesliga. When Stoger was dismissed on 3 December, Cologne were in 18th place - bottom of the table - with three points from three draws in their 14 games.
On 9 December, Cologne’s first fixture after Stoger’s departure highlighted the depth of the malaise. They were 3-0 up at home at the RheinEnergieSTADION within 30 minutes against 16th placed Freiburg. But the hosts conceded two penalties in second-half stoppage time to lose 4-3.