Ginter, a 2014 World Cup winner who also won the Confederations Cup with Germany on Sunday, joined Dortmund in 2014 but failed to hold down a regular starting spot.
With next year's World Cup on the horizon, the 23-year-old is eager for more first-team football to remain in contention for a spot in the squad, opting to miss out on a chance to play in the Champions League with Dortmund.
"Matthias Ginter came to us and asked for a transfer due to the current competition for a spot in our defence," Dortmund sports director Michael Zorc said.
"We met that request. We thank him for his engagement and wish him all the best."
There were no details regarding the length of his contract but German media reported the transfer fee at 17 million euros (14.94 million pounds).
(Reporting by Karolos Grohmann; Editing by John O'Brien)
