He was part of Jurgen Klopp's backroom team at the German outfit and he was linked with a move to Liverpool after leaving Dortmund last week.
Huddersfield sacked Chris Powell on Wednesday following their 2-2 draw with Reading and the Yorkshire club claimed they wanted "a change of direction and a new approach".
Wagner will now start his new role on Monday and chairman Dean Hoyle is excited by the appointment.
"David's football philosophy is directly in line with that of the club; he fits for what we need," he told the club's official website.
"It is a new departure for us. He will be head coach; he is the club's first from outside the UK and Ireland and he brings a new approach and new ideas.
"In his own words, and as we hope will be seen in practice, his playing style echoes the one that has brought Borussia Dortmund such success over the last five years.
"Although the players are different, there are few fans who have watched that style in action and not found it enthralling to watch. I believe that will excite our fans."