The much-travelled Papastathopoulos, 24, has penned a five-year deal for an undisclosed fee.
"We are delighted that Sokratis has decided to join Borussia Dortmund. He is a flexible player capable to play in a variety of positions in defence who we believe has tremendous potential," Dortmund sporting director Michael Zorc said in a club statement.
Dortmund, beaten 2-1 by German rivals Bayern Munich in Saturday's Champions League final having also lost their Bundesliga title to the Bavarians, have moved quickly to shore up their defence with Felipe Santana moving to rivals Schalke.
The Brazilian, 27, has signed a deal with Schalke until 2016 with the fee again undisclosed.
"Felipe expressed the wish to leave Dortmund. We would like to thank him for five great, successful years and we wish him all the best for his future," added Zorc.
Schalke finished fourth in the Bundesliga this term, 11 points behind second-placed Dortmund.
Jurgen Klopp's Dortmund could well see more remodelling following their Champions League final defeat with Bayern's retiring coach Jupp Heynckes hinting at Wembley that the club are close to signing Dortmund striker Robert Lewandowski.
Germany midfielder Mario Gotze has already announced he will leave Dortmund for Bayern next month.
