The 26-year-old joins the Bundlesliga club on a three-year deal after spending nine years with the Gunners, in which he scored 45 goals in 171 appearances.
It was a spell which also included loans at Birmingham, Sunderland and Juventus.
"We want to play a good role in all three competitions this season, and to do this we need players who already know what this kind of challenge is all about," Wolves manager Dieter Hecking said.
"Nicklas embodies precisely the kind of striker we were looking for. He fits the profile and is going to strengthen our squad."
Wolfsburg managing director Klaus Allofs described Bendtner as “a striker at the best age, who already was able to gather a lot of international experience in his career, which did not always run in a straight line."
Bendtner has been given squad number three at Wolfsburg, the 2009 Bundesliga champions who finished fifth last season.