Ginter, part of the successful FIFA World Cup squad in Brazil, was one of few bright spots for Freiburg last term - starting every Bundesliga game in the 2013-14 season.
Since graduating from the club's youth system, he has featured 70 times for Freiburg in three seasons.
Together with other recent acquisitions Ciro Immobile and Adrian Ramos, Ginter will be tasked with helping Dortmund challenge Bayern Munich's domestic dominance.
"Today a childhood dream comes true," he told the club's official website.
"I was always a big BVB fan and now get to wear the jersey of my favorite team. In Dortmund, I would like to take the next step in my sporting development.
"I am already looking forward to the incredible atmosphere at Signal Iduna Park and being a part of this wonderful team."
Ginter will link up with fellow World Cup winners Mats Hummels, Roman Weidenfeller, Erik Durm and Kevin Grosskreutz at Dortmund.
Sporting director Michael Zorc says the defender - Germany's youngest ever World Cup winner - will add quality and depth to their defensive ranks.
"Matthias has always been a strong and flexible player and German top talent is always interesting to us," he added.
"We are pleased and also a little proud that he has been well known so early to Borussia Dortmund.
"BVB, playing in three competitions, is very ambitious and has deliberately decided to go with four strong central defenders in the coming season."
