Kurt, an attacking midfielder who is considered among the most talented young players in Germany and is an Under-19 international, was Bayern's third signing this week.
Gladbach were unwilling to sell him but the player, whose contract ran to 2016, had repeatedly said he wanted to move to Munich.
Defender Mehdi Benatia and midfielder Xabi Alonso have also been signed as Bayern look to fill the gaps left by a string of injured players, including Bastian Schweinsteiger and Javi Martinez.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
Share
