Dortmund said that Stoeger, and assistant coaches Manfred Schmid and Joerg Heinrich, had signed contracts through to the end of June 2018.
Dutchman Bosz, who had been in charge for six months, was dismissed a day after Dortmund were jeered off the field following a 2-1 defeat by Werder Bremen, leaving them without a Bundesliga win since late September.
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"We decided yesterday evening in a chat with Peter Bosz that we must let him go immediately," Dortmund's CEO Hans-Joachim Watzke told a news conference. "He was emotional, but took it calmly."
Stoeger was immediately presented to the media. "I'm enormously happy to be allowed to coach this team, in this stadium," he said.
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