"We are delighted to have him with us," declared Wolfsburg sporting director Klaus Allofs after making official a transfer that had been announced in German media reports on Wednesday.
The 26-year-old has signed a five-year deal at the Volkswagen Arena as he looks to cement his place in the Brazil squad ahead of next year's World Cup.
"I spoke to (Brazil coach Luiz Felipe) Scolari. He gave me his opinion and that allowed me to come to the right decision," Luiz Gustavo said.
No transfer fee has been announced, although Allofs described reports that they had agreed to pay €22 million ($29.4 million) as well as an annual salary of €8 million as being "a long way from the reality".
He had fallen down the pecking order at Bayern during their run to the treble of Champions League, Bundesliga and German Cup last season and the summer arrivals of Mario Göetze and Spain's Thiago Alcantara had even further reduced his chances of making Pep Guardiola's team.
Luiz Gustavo first arrived in Germany with Hoffenheim before moving to Bayern in January 2011 for €17 million. He made a total of 36 appearances last season for the Bavarians and also helped his country win the Confederations Cup in June.
He won his 12th cap in the midweek friendly in Switzerland, which Brazil lost 1-0.