The South Korean striker initially joined the Germans on loan in January 2013 before returning to Wearside in the summer but has now completed a transfer to the Bundesliga club for an undisclosed fee.
Sunderland boss Gus Poyet wished the 22-year old all the best for the future.
"We wish him well because for some reason, I don't know, it don't work out for him at Sunderland, so I hope it works at his next club,” he said.
Ji joined the Black Cats from Chunnam Dragons in June 2011 and made 28 appearances in all competitions for just two goals.
During his loan spell with Augsburg last season, he netted five times in 17 outings for the Bavarian outfit.
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