The Champions League finalists have completed the signing of the Greek defender, with the Brazilian centre-back moving to the Veltins Arena
The 24-year-old's representative already revealed last week that his client was on the verge of completing his move to BVB and the defender has now signed a five-year deal with the Champions League runners-up.
"We are very pleased that Sokratis has decided to join Borussia Dortmund. He can play in several positions in defence and he has a lot of potential," sporting director Michael Zorc commented.
Sokratis is a product of the AEK Athens youth academy and represented Niki Volos, Genoa and AC Milan before joining Werder in the summer of 2011. He had since made 59 Bundesliga appearances for Bremen, netting two goals in the process.
Meanwhile, Felipe Santana has left Dortmund for Ruhr rivals Schalke as he looks to get more playing time elsewhere in a deal believed to be worth €1 million.
"I would like to thank the fans, players and everybody else at the club for my time here. It was a very hard decision to leave BVB," he explained.
"I need regular playing time, though, if I want to make it into the Brazilian national team and that's my goal."
Santana had joined Dortmund from Figueirense in the summer of 2008 and had since made over 100 official appearances for BVB.
The defender has signed a three-year deal with his new club.