The 34-year-old Friedrich, who signed a deal until the end of the season, had been training with the Bundesliga club for the past few days and was without a side following his release from Bayer Leverkusen at the end of the last campaign.
"We are reacting to the injuries we have in our defence," Dortmund sports director Michael Zorc said in a statement. "Manuel Friedrich has a lot of experience and has left a very good impression in training."
Friedrich is no stranger to Juergen Klopp, having had two spells at Mainz 05 under the Dortmund coach. He also played for Werder Bremen and was at Leverkusen from 2007.
"I am really looking forward to wearing the Dortmund shirt when entering the stadium," Friedrich, who won nine caps for Germany, said.
"I only had that pleasure of being a visitor here and to have the yellow wall (standing home fans) supporting and not against you must be a sensational feeling. I look forward to a cool time in black and yellow."
Dortmund have seen their entire backline compromised in the past few weeks with central defender Mats Hummels becoming the latest victim after tearing heel ligaments in Germany's 1-0 win against England on Tuesday.
Left back Marcel Schmelzer was ruled out for three weeks with a muscle injury picked up in the same game, while central defender Neven Subotic suffered a cruciate ligament injury two weeks ago and will be out until the end of the season.
Right back Lukasz Piszczek only recently returned to training following double hip surgery in the off-season.
Dortmund are second in the Bundesliga, four points behind Bayern Munich, whom they host in the biggest game of the season so far on Saturday.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
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