A four-year deal has been signed by the full-back from the German club.
A former England Under-21s defender is moving for a reported $10 million.
Richards was part of the team that helped them to a 32nd Bundesliga title.
"I'm thrilled to be back in England and I can't wait to get started at Forest."
There's great ambition for the return of the premier league for the club.
The City Ground is an amazing place that I can now call home after playing against Forest there in the past. I'm excited to join the squad this week and start preparing for the new season.
Richards played 104 times for the Royals before moving to Germany.
He is the fifth summer signing for Forest.
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