The 22-year-old has agreed a five-year contract with the Bundesliga champions, who have parted with €17.5 million in order to bring Reus to the Westfalenstadion.
"In Marco Reus we sign our absolute preference for an offensive player," Dortmund sporting director Michael Zorc told the club's official website.
"We are delighted that Marco has chosen BVB, despite top class competition."
Both Manchester United and Arsenal were reported to have been keeping tabs on the situation of Reus, although it is unclear if either ever made a formal approach.
The Guardian initially claimed that Sir Alex Fergsuon and Arsene Wenger held a genuine interest in the Germany international, and it was later confirmed that the latter was showing particular interest.
Gladbach boss Lucien Favre said he had heard from the Arsenal boss regarding Reus, following a tip off from former Gunners 'keeper Jens Lehmann.
However, Reus is delighted to be able to seal a switch back to his hometown club.
"To me it is important to clarify that this is not a decision against Gladbach. I have had a wonderful time here," Reus said.
"Borussia have given me the chance to prove myself in the Bundesliga and to develop into the player I am today."