Ji, who will spend the rest of the 2013/14 season at FC Augsburg after joining die Fuggerstädter from Sunderland AFC on a short-term deal, will sign a four-year contract with Jürgen Klopp's team on 1 July.
"Dong-Won Ji is a professional who can play in several positions across the attack," said BVB sporting director Michael Zorc. "We're delighted to be getting this talented player on a free transfer in time for the new season."
Ji scored five goals in 17 appearances for Augsburg during a loan spell in the second half of the 2012/13 campaign. The 22-year-old has also scored eight times in 26 appearances for South Korea.