The Denmark international left Arsenal at the end of last season after a nine-year period that also included three loan spells at Juventus, Sunderland and Birmingham City.
"We want to have a good run in all three competitions we are in this season and for that we need players who know these challenges and are used to them," said Wolfsburg coach Dieter Hecking at the player's official presentation.
"Nicklas is exactly the type of player we were looking for. He fits our profile and will strengthen the team."
Bendtner, 26, made a total of 171 appearances and scored 47 goals after joining the Premier League team from Copenhagen in 2005.
(Reporting by Karolos Grohmann, editing by Tim Collings)
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