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Arsenal had a £17.2 million bid accepted for the Brazilian earlier this week, but he has elected to stay in Germany and move to the Volkswagen arena.
Gustavo had fallen out of favour in Bavaria following the arrival of Pep Guardiola, who brought in Thiago Alcantara to complete a midfield already brimming with talent.
Bastian Schweinsteiger, Javi Martinez, Toni Kroos and Xherdan Shaqiri were already vying for central roles at the Allianz Arena.
Gustavo joined Bayern from Hoffenheim in January 2011, making over 60 Bundesliga appearances for die Roten and winning the treble in 2012-13.
The Brazilian midfielder joins compatriots Naldo, Diego and Felipe Lopes at Wolfsburg.