Wagner guided Huddersfield into the top flight in 2016-17 for the first time in 45 years after winning the Championship playoff final against Reading. With the odds stacked against him, he then kept them in the top flight last season.
The current campaign has been more difficult, however, with Town winning two of their 23 matches and currently sitting 10 points adrift of safety at the bottom of the table.
Siewert has previously coached Germany's international youth sides and held senior management roles at VfL Bochum and Rot-Weiss Essen apart from his role in charge of Dortmund's reserves.
"Jan's name came to our attention in his previous role as assistant manager and under-19 Coach at VfL Bochum. We first spoke with him over two years' ago and we've kept in communication since, watching his progress with interest," Town's chairman Dean Hoyle told the club's official website.
Hoyle added that Siewert had been tasked with enhancing the high-pressing identity that Wagner had instilled in the team, while his reputation for promoting youth had also made him an attractive candidate.
"Many of (Siewert's) core philosophies and beliefs about how he wants his teams to play match our own. He likes high-effort, high-intensity, high-pressing football that is good to watch," Hoyle said.
"In the short-term, we will continue to fight as hard as possible against relegation from the Premier League. We're not giving up on that.
"We will also plan for the medium and long-term, whatever the outcome. Jan is committed to us and is excited to take on the challenges we have ahead, whatever they look like."
(Reporting by Simon Jennings in Bengaluru; Editing by Hugh Lawson)
