Delaney, who only arrived in Germany last summer after joining Bremen from Copenhagen in his native Denmark, has signed a four-year contract until 2022.
"For me, Dortmund is one of the top 10 clubs in Europe and one of the top two clubs in Germany - and the stadium is the best in Europe!" he added.
"I promise that I will always play with a lot of heart and I'm already extremely looking forward to the sporting challenge at BVB and I'm hoping to win titles in the black and yellow jersey."
Speaking on the signing, sporting director Michael Zorc commented, "Borussia Dortmund has always had first class experience with Danish internationals.
"Thomas Delaney is a physically and character strong player, who fits with his open nature and his pronounced will to win outstanding in our team and the entire BVB.
"He will enrich our game with his physical presence."
Delaney is part of the Denmark squad for this summer's World Cup in Russia and will be in action against Peru, Australia and France in the group stage later this month.