The South Korean international was released by the Black Cats last week after failing to make much of an impact on Wearside scoring just twice in 28 appearances.
Sunderland turned down a £4million bid from Dortmund in the summer for the striker when Paolo Di Canio was in charge at the Stadium of Light, but new boss Gus Poyet decided Ji was surplus to requirements.
The striker will officially join the Bundesliga club on the 1 July, the same date that current Dortmund striker Robert Lewandowski will join bitter rivals Bayern Munich.
The striker will play for fellow German side Augsburg for the remainder of the season after enjoying successful loan spell there last year after he agreed a six month deal there, with Sunderland allowing their man to leave.
“Dong-Won Ji is a professional who is used on the offensive in several positions. We are pleased to be able to undertake these talented players free transfer to the new season,” says BVB sporting director Michael Zorc.