The Bundesliga outfit made their interest in the Brazil international midfielder known early, placing them towards the front of the transfer queue.
They were, however, soon joined in the chase for the 26-year-old's signature by Arsenal - who were reported to have lodged a bid of over £17million.
Gustavo admitted to being open to the idea of swapping life in Germany for that in England, but the Gunners have been left frustrated in their transfer endeavours once again.
Wolfsburg have wrapped up a deal for a man who helped Bayern to an historic Treble in 2012/13, and have tied him down until 2018.
Gustavo has moved for an undisclosed fee and will be looking to hit the ground running at his new employers - with a home World Cup in 2014 very much in his thoughts.
A statement released on Wolfsburg's official website read: "Luiz Gustavo has transferred with immediate effect from Bayern Munich to Vfl Wolfsburg.
"The 26-year-old midfielder has signed a contract until 2018 and will be officially presented today (Friday) in Wolfsburg.
"Both sides have agreed to remain silent about the transfer arrangements."