The 21-year-old midfielder is believed to have been a long-time target for Liverpool, who reportedly had a bid rejected by Gladbach at the end of last season.
It has now been confirmed that the Reds have missed out on signing the German Under-21 international as the young player has opted to move to the Westfalenstadion on a five-year deal.
Gladbach's director of sport Max Eberl told reporters: "A decision has been made - Mahmoud Dahoud will be leaving us. He has chosen to join Borussia Dortmund. It was important for the player and the club that a decision was reached. Now it's off our minds and we can move on.
"This transfer shows that we're doing good work. Our task is to develop talents and be successful. We will reinvest the money we get for Dahoud and try to find a good replacement for him."
The midfielder made his senior debut in 2014 and has caught the eye, particularly in the last two seasons where he has emerged as a regular feature.
In this campaign, Dahoud has made 32 appearances, four of which were in the Champions League group stage.