Douglas Costa joins Bayern Munich from Shakhtar Donetsk

Douglas Costa has signed a contract at Bayern until 2020

German champions Bayern Munich have signed Brazil midfielder Douglas Costa from Shakhtar Donetsk.

Costa, 24, has moved for a fee of £21m according to the Ukrainian club and signed a five-year deal with Pep Guardiola's side.

"A dream has come true for me today," said Costa, who has returned from Copa America duty with Brazil.

The transfer could increase speculation linking Bayern midfielder Bastian Schwensteiger with Manchester United.

Guardiola, who guided Bayern to their 25th Bundesliga title last season, has plenty of midfield options, including France's Franck Ribery and Spain internationals Thiago Alcantara, Xabi Alonso and Javi Martinez, meaning Schweinsteiger, 30, may feature less regularly.

The Germany international only played 20 league games in 2014-15, his lowest tally since 2002, when he signed professional terms with the club.

Costa scored 29 goals in 149 league games for Shakhtar, where he won the title five times.

"Douglas Costa will be good for our team," said Bayern sporting director Matthias Sammer. "He has great technical ability, a powerful left foot, he is very agile and extremely quick."