The 22-year-old had a five-month loan spell with Augsburg last season, scoring five goals in 17 games, and in a convoluted deal has joined the club again on a permanent short-term deal until the end of the season.
However, once that short-term deal expires, the forward will move to Juergen Klopp's men on a four-year deal.
"Dong-won Ji is a professional who can play in several positions across the attack," said BVB sporting director Michael Zorc.
"We're pleased to be getting this talented player on a free transfer in time for the new season."
Ji joined Sunderland from K-League side Chunnam Dragons in June 2011 and played 28 times for the Black Cats, scoring twice.