The 26-year-old has spent the last one-and-a-half seasons with Bremen, with seven goals being scored in 49 appearances for the Bundesliga outfit.
Delaney had interest from the Premier League but the player has instead opted to move to Dortmund, who have spent in the region of £17.5m.
The Denmark international told the club's official website: "I've always wanted to play in the Premier League at some stage and I've had offers too, but when Dortmund came calling, I didn't have to think twice.
"For me, BVB are one of the top 10 clubs in Europe and one of the top two clubs in Germany and the stadium is definitely the best in all of Europe."
Brighton & Hove Albion were allegedly one of the English clubs to make an offer for Delaney.