The 40-year-old German, who was sacked by Wolfsburg in April, will begin his role at the John Smith's Stadium on June 1.
Rebbe was the Bundesliga's second-youngest sporting director when he joined Wolfsburg in 2016, having previously worked at Werder Bremen.
"As sporting director, Rebbe will work closely with head coach David Wagner and report to the board on the recruitment of players and the monitoring of football operations such as scouting, analysis, sports science and medicine," Huddersfield wrote in a statement.
"Rebbe will also work closely with academy manager Leigh Bromby to drive the development of the club's youth system in its new form."
Rebbe's departure from the German club - who are involved in the relegation playoff in the Bundesliga for the second season in a row - came after they failed to recruit general manager Horst Heldt from Hannover.