The 20-year-old centre-back, who was a regular in the B team over previous seasons, has joined the 2. Bundesliga outfit, who are managed by former Saints forward Uwe Rösler.
An Austria youth international, Klarer joined Southampton in 2016, signing from Rapid Wien.
He initially played in the Under-18s set-up before progressing into what was previously known as the Under-23s.
Klarer joins Fortuna Dusseldorf in an outright deal.