The German side announced the deal on Wednesday after the two clubs agreed a fee for the Brazilian attacker
Douglas Costa has completed his move to Bayern Munich after the Bundesliga side agreed a €30 million fee with Shakhtar Donetsk.
The Ukrainian side revealed an agreement with the Bundesliga champions had been reached on Wednesday, thanking the Brazil international for his five years of service.
"Shakhtar Donetsk and Bayern Munich have agreed all the necessary formalities regarding Douglas Costa’s move to the German club," the club said in a statement. "The transfer fee for the Brazilian midfielder is €30m.
"Shakhtar thanks Douglas for the time spent in the team and wishes him every success with the new club."
Moments later, Bayern tweeted the move had been completed and that the attacker has signed a deal which ties him to the club until 2020.
"For me, today a dream came true," Douglas Costa told the Bavarians' official website. "I am proud to play for Bayern, a club where many famous Brazilians have played before.
"I am looking forward to being part of a great team and I will do everything to meet the expectations."
Bayern sporting director Matthias Sammer added: "Douglas Costa will be a valuable addition to our team. He has got exceptional technical skills, a strong left foot, he's very agile and extremely fast.
"Douglas Costa has decided to take the next step in his career after having played in Brazil and Ukraine. We will support him in every aspect."
The 24-year-old will be an additional wing option for coach Pep Guardiola, whose Bayern XI was hindered last season by the lack of options when Arjen Robben and Franck Ribery were injured.
