A ranar 1 ga Yuli, 2015, Bayern Munich ta sanar da cewa sun sanya hannu kan Costa a kan kudin canja wuri na € 30 miliyan. Costa ya sanya hannu kan kwangilar shekaru biyar. Kudin canja wuri na € 30 miliyan shi ne na huɗu mafi girma a tarihin Bayern. An ba shi lambar 11 da Xherdan Shaqiri ya riga ya sa. Ya fara bugawa a ranar 1 ga Agusta a cikin 2015 DFL-Supercup a waje da VfL Wolfsburg, yana tsallakewa Arjen Robben don buɗe ƙidaya a cikin ƙarshe 1<unk>1 Draw; ya zira kwallaye a ƙoƙarinsa a cikin bugun bugun jini na gaba, amma tawagarsa ta yi asara duk da haka. Costa ya zira kwallaye na farko na Bundesliga a wasan farko na Bundesliga a cikin nasara na 5<unk>0 a kan Hamburger SV. A ranar 21 ga Mayu, 2016, Costa ya zira kwallaye na farko na bugun jini a kan Borussia Dortmund a duk faɗin gasar cin kofin DFB na 2016 kuma ya sami nasara a gasar cin kofin Bundesliga ta Bayern.
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