Augsburg parted ways with Enrico Maassen on Monday after over a year in charge, the 39-year-old leaving the club 15th in the standings after seven games.
Thorup managed Denmark's Under-20 and Under-21 teams, and spent nearly two years in charge of Copenhagen, leading them into the 2022-23 Champions League.
"I had very constructive and goal-oriented discussions with those at the club and I immediately felt that Augsburg was the right next step for me," Thorup told the club website.
Augsburg travel to promoted Heidenheim, 10th in the table, on October 22nd.