Siewert takes charge of a club who face a near-impossible job to avoid relegation, sitting bottom of the Premier League, 10 points from a position of safety, having won just two of 23 matches.
Wagner left by mutual consent on January 14 after more than three years in charge, having taken the club into the top division for the first time since 1972, then kept them there last season.
Julian Winter, Huddersfield’s chief executive, said that Wagner had indicated before Christmas that he needed to take a break from management.
Winter said: “David is a good man. We maybe first had a conversation four weeks ago, something of that order.
“David, being the human being that he is, sort of said building up to a January transfer window: Does the club want to adapt, think about different things? The maturity of that conversation was exactly as it was publicised.”
Winter added that Huddersfield had made preparations so that the club would not suffer off the field in the event of relegation.
He said: “To be blunt, this club has been prepared for getting into the Premier League and it will be prepared if it is not in the Premier League.
“We retained our status last season, which was fabulous. But we know that if this club does get relegated, it doesn’t fall into crisis. There aren’t fire sales.”