The Bundesliga giants have announced the capture of the Germany international on a five-year deal
Freiburg president Fritz Keller revealed earlier this week that they were in advanced talks with BVB and the 20-year-old has now signed a contract until June 2019 after passing his medical.
"Matthias is a strong and versatile German youngster who has always been a very interesting player to us," Dortmund sporting director Michael Zorc commented.
"We are very pleased and proud that Matthias has decided to join Dortmund.
"BVB are playing in three different competitions, are full of ambition and have deliberately decided to start the new season with four strong centre-backs."
Ginter, who was part of the Germany team that was crowned world champions earlier this month, came through the ranks of the Freiburg youth academy and had developed into a key player at the Mage Solar Stadion since making his first-team debut in January 2011.
"This is a dream come true for me. I have always been a Dortmund fan and will now get the chance to wear the jersey of my favourite team," Ginter said.
"I want to take the next step in my development here at Dortmund. I am looking forward to the great atmosphere at the Signal Iduna Park. I have only heard positive things about Dortmund and I'm keen to get started after my holiday."
Ginter will be wearing the No.28 jersey at Dortmund.