The 22-year-old joins the Champions League entrants after just one goal in 40 games for Leeds following his move from Red Bull Salzburg last season.
Aaronson will link up with USA team-mate Jordan Pefok at the Stadion An der Alten Forsterei this coming season.
Aaronson follows Frankfurt defender Robin Koch in heading for the German league on loan following Leeds' relegation to the Championship last season, while Diego Llorente has joined Italian club Roma.