The Denmark international, 26, has signed a three-year contract with the German side.
Bendtner made 168 appearances in all competitions for Arsenal, scoring 47 goals.
Director of sport Klaus Allofs said: “Nicklas Bendtner is at the very best possible age for a striker.
“During his career – which wasn’t always so straightforward – he managed to gather a great deal of international experience and he adds further quality to our attack.”
Bendtner spent loan spells with Birmingham city, Sunderland and Juventus during his time at Arsenal.
He has chosen the No. 3 shirt, having previously worn No. 52 at Arsenal.
"My mother chose the number for me," he explained.
- Sports & Recreation
- Klaus Allofs