On 1 July 2015, Bayern Munich announced they had signed Costa for a transfer fee of €30 million. Costa signed a five-year contract. The €30 million transfer fee was the fourth-highest in Bayern's history. He was given the number 11 shirt previously worn by Xherdan Shaqiri. He made his debut as a starter on 1 August in the 2015 DFL-Supercup away to VfL Wolfsburg, crossing for Arjen Robben to open the scoring in an eventual 1–1 draw; he netted his attempt in the subsequent penalty shoot-out, but his team lost nonetheless. Costa scored his first Bundesliga goal in his first Bundesliga game in a 5–0 win against Hamburger SV. On 21 May 2016, Costa scored the winning kick of the penalty shootout against Borussia Dortmund to win the 2016 DFB-Pokal Final and secure a league and cup double for Bayern.