The Denmark international has signed a three-year contract with the Bundesliga club, 12 months after being denied a move away from the Gunners after they failed to sign a replacement.
"Nicklas Bendtner is a striker in his prime, who has already collected a lot of international experience in his career, which has not always been straightforward," Vfl sporting director Klaus Allofs said of the move.
"He will increase our attacking quality even further his quality."
Coach Dieter Hecking added: "We want to play a big role in all three competitions this season, but we need players who are used to these challenges.
"Nicklas embodies exactly the type of striker we were looking for. He fits our requirements and will strengthen our squad."
Bendtner moved to Arsenal as a teenager in 2004 and made over 100 Premier League appearances for the Gunners.
Though he spent the last year at the Emirates, he had loan spells at Sunderland in the 2011-12 season and Juventus for the following campaign.